audio
audioduration (s) 0.83
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one over n cubed
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$\frac{1}{n^{3}}$
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https://www.youtube.com/watch?v=MK_0QHbUnIA
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one plus one over two plus all the way up to one over n minus one plus 1 over n
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$1+\frac{1}{2}+\mathrm{\ldots}+\frac{1}{n-1}+\frac{1}{n}$
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https://www.youtube.com/watch?v=MK_0QHbUnIA
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a half plus a third
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$\frac{1}{2}+\frac{1}{3}$
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https://www.youtube.com/watch?v=MK_0QHbUnIA
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1 over n squared plus 1 square root
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$\frac{1}{n^{2} + 1}$
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https://www.youtube.com/watch?v=MK_0QHbUnIA
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sum one over n to the five-halves
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$\sum\frac{1}{n^{5/2}}$
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https://www.youtube.com/watch?v=MK_0QHbUnIA
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one times one plus two times minus two plus minus three times one
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$1\times1+2\times(-2)+(-3)\times1$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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x plus 3y plus z equals zero
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$x+3y+z=0$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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minus 2x minus z will be x plus 3y plus z
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$-2x-z\operatorname{=}x+3y+z$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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x equals minus 3t
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$x=-3t$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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y equals 3t
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$y=3\mathfrak{t}$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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z equals negative 6t
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$z\!=\!-6t$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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dr dt dot r plus r dot dr dt
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$\displaystyle \frac{dr}{dt}\cdot{r}+r\cdot\frac{dr}{dt}$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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d by dt of r dot r is zero
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$\displaystyle \frac{d}{dt}(\mathbf{r}\cdot\mathbf{r})=0$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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minus v dot v
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$-\mathbf{v}\cdot\mathbf{v}$
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https://www.youtube.com/watch?v=U1EcnfTKXJ0
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f of x y equals one over x plus y
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$f(x,y)=\frac{1}{x+y}$
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https://www.youtube.com/watch?v=dK3NEf13nPc
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f of x y equals one minus x squared minus y squared
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$f(x,y)=1-x^{2}-y^{2}$
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https://www.youtube.com/watch?v=dK3NEf13nPc
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z equals one minus x squared minus y squared
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$z=1-x^{2}-y^{2}$
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https://www.youtube.com/watch?v=dK3NEf13nPc
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x squared plus y squared equals one
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$x^{2}+y^{2}=1$
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https://www.youtube.com/watch?v=dK3NEf13nPc
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f prime at x0 times delta x
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$ f^{\prime}(x_{0})\Delta x$
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https://www.youtube.com/watch?v=dK3NEf13nPc
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d dy of y to the n times dy dx
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$\displaystyle (\frac{d}{dy}y^{n})\frac{dy}{dx}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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m x to the n minus one
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$(mx^{m-1})$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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n y to the n minus 1
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$(ny^{n-1})$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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x to the m minus one
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$\mathcal{x}^{m-1}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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x to the m over n times n minus 1
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$x^\frac{m}{n}{(n-1)}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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minus one plus m over n
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$-1+\frac{m}{n}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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a minus one
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$\mathsf{a}-1$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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a x to the a minus one
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$(ax^{a-1})$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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y is equal to plus or minus square root of 1 minus x squared
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$y =\pm\sqrt{1-x^{2}}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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2 x plus 2 y y prime
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$2x+2yy^{\prime}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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y to the fourth plus xy squared minus two is equal to zero
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$y^{4}+xy^{2}-2=0$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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four y cubed y prime
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$4y^{3}y^{\prime}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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minus y squared divided by 4y cubed plus 2xy
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$-\frac{y^{2}}{4y^{3}+2xy}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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y to the fourth plus xy squared minus 2 is equal to zero
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$y^{4}+xy^{2}-2=0$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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minus 1 squared divided by 4 times 1 cubed plus 2 times 1 times 1
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$\frac{(-1)^2}{4\times1^{3}+2\times1\times1}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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tan inverse x is equal to pi over two
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$\operatorname{\tan}^{-1}x=\frac{\pi}{2}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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d by dy tan y times dy dx
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$\displaystyle \frac{d}{dy}\tan(y)\frac{dy}{dx}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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d by dx of tan inverse of x
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$\frac{d}{dx}(tan^{-1}(x))$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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cosine squared of tan inverse x
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$\cos^{2}(tan^{-1}x)$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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one over 1 plus x squared
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$\frac{1}{1+x^{2}}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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d by dx of tan inverse x is equal to one over 1 plus x squared
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$\frac{d}{dx}(tan^{-1}x)=\frac{1}{1 + x^{2}}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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1 over square root of 1 minus x squared
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$\frac{1}{\sqrt{1-x^{2}}}$
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https://www.youtube.com/watch?v=5q_3FDOkVRQ
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a to the x1 plus x2 is a to the x1 times a to the x2
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$\displaystyle a^{x_1 + x_2} = a^{x_{1}}\cdot a^{x_{2}}$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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a to the x plus delta x
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$a^{x+\Delta x}$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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M of a is equal to the limit as delta x goes to 0 of a to the delta x minus 1 divided by delta x
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$M(a)=\lim_{\Delta x\to 0}\frac{a^{\Delta x}-1}{\Delta x}$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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k times f prime of kx
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$k\cdot f^{\prime}(kx)$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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e to the log x is equal to x
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$\mathrm{e}^{\log x}=x$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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d by dx e to the w
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$\frac{d}{dx}\mathbf{e}^{w}$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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e to the power log a to the power x
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$(e^{\ln a})^{x}$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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d by dx of a to the x is equal to d by dx of e to the x log a
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$\frac{d}{dx}(a^{x})=\frac{d}{dx}(e^{x}\log a)$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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log a times e to the x log a
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$\log a\,\mathrm{e}^{x\log a}$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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The derivative with respect to x of 2 to the x is log 2 times 2 to the x
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$\frac{d}{dx}(2^{x})=\log{2}(2^{x})$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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log 10 times 10 to the x
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$\log 10\times 10^{x}$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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log u prime is equal to u primie over u
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$\log u^{\prime}=u^{\prime}/u$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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u prime is equal to u times log a
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$u^{\prime}=u\cdot\log a$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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v prime is equal to v times 1 plus log x
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$v^{\prime}=v(1+\log x)$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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d by dx x to the x
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$(\frac{d}{dx}(x^{x}))$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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one plus one over n to the power n
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$(1+\frac{1}{n})^{n}$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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n log one plus one over n
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$n\log(1+1/n)$
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https://www.youtube.com/watch?v=9v25gg2qJYE
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one plus one over k to the kth power
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$(1+\frac{1}{k})^{k}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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ln of one plus one over k
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$\ln(1+\frac{1}{k})$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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e to the r log x prime
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$\mathrm{e}^{r}\log x^{\prime}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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u times r divided by x
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$u\times\mathbb{r}/x$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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r x to the r minus one
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$rx^{r-1}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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y is ten x plus b
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$y=10x+b$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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fifty t plus ten a plus b
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$50t+10a+b$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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minus v to the minus 2 times v prime
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$-v^{-2}v^{\prime}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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x to the ten plus eight x
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$x^{10}+8x$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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e to the x tan inverse x
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$\mathrm{e}^{x}{\tan^{-1}x}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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x divided by 1 plus x squared
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$\frac{x}{1+x^{2}}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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the limit as delta x goes to 0 of f of x plus delta x minus f of x divided by delta x
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$\displaystyle \lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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one over one plus y squared times y prime
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$\frac{1}{1+y^{2}}y^{\prime}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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one divided by the square root of one plus x squared
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$1/\sqrt{1+x^{2}}$
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https://www.youtube.com/watch?v=eHJuAByQf5A
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x zero plus f prime of x zero x minus x zero
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$\displaystyle x_{0}+f^{\prime}(x_{0})(x - x_{0})$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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y equals cosine x
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$y=\cos x$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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y equals e to the x
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$y=\mathrm{e}^{x}$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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y equals one plus x
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$\displaystyle y=1+x$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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f prime is one over one plus x
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$f^{\prime}=\frac{1}{1+x}$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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r one plus x to the r minus 1
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$(r\cdot{1+x}^{r-1})$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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e to the minus 3x divided by square root 1 plus x
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$e^{-3x}/\sqrt{1+x}$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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e to the minus three x one plus x to the minus a half
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$e^{-3x}(1+x^{-1/2})$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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one minus three x minus a half of x plus three halves x squared.
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$1-3x-\frac{1}{2}x+\frac{3}{2}x^{2}$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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t prime is equal to t divided by the square root of 1 minus v squared over c squared
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$t^{\prime}= t/\sqrt{1-v^{2}/c^{2}}$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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v squared over c squared
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$\frac{v^{2}}{c^{2}}$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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t times 1 plus a half v squared over c squared
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$t(1+\frac{1}{2}\frac{v^{2}}{c^{2}})$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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y equals one minus a half x squared
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$y=1-\frac{1}{2}x^{2}$
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https://www.youtube.com/watch?v=BSAA0akmPEU
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one plus a half v squared over c squared
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$1+\frac{1}{2}v^{2}/c^{2}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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f double prime of zero divided by two
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$f^{\prime\prime}(0)/2$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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sine x is approximately x
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$\sin x\approx x$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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cosine x is approximately one minus a half x squared
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$\cos x\approx 1-\frac{1}{2}x^{2}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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e to the x is approximately one plus x plus a half x squared
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$e^{x}\approx 1+x+\frac{1}{2}x^{2}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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x minus a half x squared
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$x-\frac{1}{2}x^{2}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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1 plus x to the power r
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$(1+x^{r})$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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one plus rx plus r times r minus one divided by two x squared
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$1+rx+\frac{r(r-1)}{2}x^{2}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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e to the minus three x one plus x to the minus a half
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$e^{-3x}(1+x)^{-1/2}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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one minus a half x plus a half times minus a half times minus three halves x squared
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$1-\frac{1}{2}x+\frac{1}{2}\times(-\frac{1}{2})\times(-\frac{3}{2})x^{2}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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f double prime is minus one over one plus x squared
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$f^{\prime\prime}=-\frac{1}{1 + x^{2}}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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r one plus x to the r minus one
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$(r\cdot 1+x^{r-1})$
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https://www.youtube.com/watch?v=eRCN3daFCmU
|
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r times r minus one x plus one to the r minus two
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$r(r-1)(x+1)^{r-2}$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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3 times 1 minus x times 1 plus x
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$3(1-x)(1+x)$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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one minus x times 1 plus x is zero
|
$(1 - x)(1 + x) = 0$
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https://www.youtube.com/watch?v=eRCN3daFCmU
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