audio
audioduration (s) 0.83
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ax plus by plus cz equals d
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$ax + by + cz = d$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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x plus 5y plus 10z equals zero
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$x + 5y + 10z = 0$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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x minus two y minus one and z plus one dot product with one, five, ten
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$[x-2,y-1,z+1]\cdot[1,5,10]$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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x minus two plus five times y minus one plus ten times z plus one equals zero
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$ (x - 2) + 5(y - 1) + 10(z + 1) = 0 $
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https://www.youtube.com/watch?v=YBajUR3EFSM
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Ax plus By plus Cz equals D
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$Ax + By + Cz = D$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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x plus y plus three z equals five
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$x + y + 3z = 5$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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x plus z equals one
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$x + z = 1$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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x plus y equals two
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$x + y = 2$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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A inverse is one over determinant of A times the adjoint matrix
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$A^{-1} = \frac{1}{\text{det}(A)} \cdot \text{adj}(A)$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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X equals A inverse B
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$X = A^{-1}B$
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https://www.youtube.com/watch?v=YBajUR3EFSM
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log two minus log one
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$\log2-\log1$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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b minus a over n
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$\frac{b - a}{n}$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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a half times one plus two thirds plus a half times a half
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$1/2\cdot1+2/3+1/2\cdot1/2$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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y0 plus 4y1 plus y2
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$\displaystyle y_0 + 4y_1 + y_2$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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a half plus n minus 1 plus a half
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$\frac{1}{2}+n-1+\frac{1}{2}$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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two pi r e to the minus r squared dr
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$2\pi r e^{-r^2} dr$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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pi minus pi e to the minus r squared
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$\pi - \pi e^{-r^2}$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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square root of pi over 2
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$\frac{\sqrt{\pi}}{2}$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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e to the minus b squared plus x squared
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$e^{-(b^2 + x^2)}$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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e to the minus b squared times e to the minus x squared
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$e^{-b^2} e^{-x^2}$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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minus b squared times the integral from minus infinity to infinity of e to the minus x squared dx
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$\displaystyle -b^2 \int_{-\infty}^{\infty} e^{-x^2} \, dx$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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integral from minus infinity to infinity e to the minus y squared dy
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$\displaystyle \int_{-\infty}^{\infty} e^{-y^2} dy$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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pi x2 squared minus x1 squared
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$\pi ({x_2}^{2} - {x_1}^{2})$
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https://www.youtube.com/watch?v=zUEuKrxgHws
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h of x equal to sine of x plus square root of 3 times cosine of x
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$h(x) = \sin(x) + \sqrt{3} \cos(x)$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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cosine x minus square root of 3 times sine x
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$\cos(x) - \sqrt{3} \sin(x)$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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square root of 3 times tan x
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$\sqrt{3} \tan(x)$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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tan of x is equal to one divided by square root of three
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$\tan(x) = \frac{1}{\sqrt{3}}$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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pi over 6
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$\frac{\pi}{6}$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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pi over 6 plus pi
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$\frac{\pi}{6} + \pi$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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minus five pi over six
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$-\frac{5\pi}{6}$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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pi over 6 minus pi
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$\frac{\pi}{6} - \pi$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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sine of x plus square root of 3 times cosine x
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$\sin(x) + \sqrt{3} \cos(x)$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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h of x equals two times one-half sine x plus square root of three over two
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$h(x) = 2 \frac{1}{2} \sin(x) + \frac{\sqrt{3}}{2}$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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pi over 3 sine x plus sine pi over 3 cosine x
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$\displaystyle \frac{\pi}{3} \sin(x) + \sin\frac{\pi}{3} \cos(x)$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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two times sine of x plus pi over three
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$2\sin(x) + \frac{\pi}{3}$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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x equals minus pi over three
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$x = -\frac{\pi}{3}$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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x equals 7 pi over 6
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$x = 7\pi/6$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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pi over 2 minus pi over 3 is pi over 6
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$\pi/2 - \pi/3 = \pi/6$
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https://www.youtube.com/watch?v=Bb-bgJdOqig
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negative sine x times x squared times the sine x
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$- \sin x \cdot x^{2} \cdot \sin x$
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https://www.youtube.com/watch?v=55ncRlBZstA
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cosine x cosine x is cosine squared x
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$\cos x \cos x = \cos^{2}x$
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https://www.youtube.com/watch?v=55ncRlBZstA
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minus x squared sine squared x
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$ -x^2 \sin^{2}x$
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https://www.youtube.com/watch?v=55ncRlBZstA
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dy dx times dx dw times dw d theta
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$ \frac{dy}{dx} \times \frac{dx}{dw} \times \frac{dw}{d\theta} $
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https://www.youtube.com/watch?v=aeQA5d3gZTI
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dw d theta is four theta to the third
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$\frac{dw}{d\theta} = 4\theta^{3}$
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https://www.youtube.com/watch?v=aeQA5d3gZTI
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cosine of theta to the fourth
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$\cos(\theta^{4})$
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https://www.youtube.com/watch?v=aeQA5d3gZTI
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two cosine of theta to the fourth times negative sine
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$2\cos(\theta^{4}) (-\sin) $
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https://www.youtube.com/watch?v=aeQA5d3gZTI
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cosine of pi over two is equal to zero
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$\cos(\pi/2) = 0$
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https://www.youtube.com/watch?v=aeQA5d3gZTI
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theta to the fourth equals pi over two
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$ \theta^{4} = \frac{\pi}{2} $
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https://www.youtube.com/watch?v=aeQA5d3gZTI
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theta is equal to pi over 2 to the 1 4th
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$\theta = (\frac{\pi}{2}) ^ \frac{1}{4}$
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https://www.youtube.com/watch?v=aeQA5d3gZTI
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y cubed plus x cubed equals three xy
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$y^{3} + x^{3} = 3xy$
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https://www.youtube.com/watch?v=fK6cu99OSEU
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four thirds cubed plus two thirds cubed is equal to three times two thirds times four thirds
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$(4/3)^{3}+(2/3)^{3}=3\times(2/3)\times(4/3)$
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https://www.youtube.com/watch?v=fK6cu99OSEU
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y minus x squared over y squared minus x
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$ \frac{y - x^{2}} {y^{2} - x}$
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https://www.youtube.com/watch?v=fK6cu99OSEU
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6 minus 16 over 4 minus 12
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$\frac{6 - 16}{4 - 12}$
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https://www.youtube.com/watch?v=fK6cu99OSEU
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d over dx of tan x is equal to secant squared of x
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$\frac{\mathrm{d}}{\mathrm{dx}}(\tan x) = \mathrm{\sec^2(x)}$
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https://www.youtube.com/watch?v=aYMt2ZVGd7g
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pi over two
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$\frac{\pi}{2}$
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https://www.youtube.com/watch?v=aYMt2ZVGd7g
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y equals arctan x
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$y = \arctan x$
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https://www.youtube.com/watch?v=aYMt2ZVGd7g
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dy dx is equal to minus 1 divided by sine y
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$\frac{dy}{dx} = -\frac{1}{\sin y}$
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https://www.youtube.com/watch?v=cdRMY39EYbs
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square root of 1 minus x squared
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$\sqrt{1 - x^{2}}$
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https://www.youtube.com/watch?v=cdRMY39EYbs
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f of x is equal to x to the pi plus pi to the x
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$f(x) = x^{\pi} + \pi^{x}$
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https://www.youtube.com/watch?v=wezQdmwolMU
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g of x is equal to natural log of cosine of x
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$g(x) = \ln(\cos(x))$
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https://www.youtube.com/watch?v=wezQdmwolMU
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pi times x to the pi minus 1
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$\pi x^{\pi - 1}$
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https://www.youtube.com/watch?v=wezQdmwolMU
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x times pi to the x minus 1
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$x \cdot \pi^{x-1}$
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https://www.youtube.com/watch?v=wezQdmwolMU
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1 over cosine x
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$\frac{1}{\cos x}$
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https://www.youtube.com/watch?v=wezQdmwolMU
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e to the x squared
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$\mathrm{e}^{x^{2}}$
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https://www.youtube.com/watch?v=wezQdmwolMU
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natural log of e to the x squared
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$\ln(e^{x^{2}})$
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https://www.youtube.com/watch?v=wezQdmwolMU
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x squared times natural log of e
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$x^{2}\cdot\ln e$
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https://www.youtube.com/watch?v=wezQdmwolMU
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natural log of e is equal to 1
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$\ln(e)=1$
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https://www.youtube.com/watch?v=wezQdmwolMU
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natural log of m times n is equal to the natural log of m plus natural log of n
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$\ln(mn) = \ln(m) + \ln(n)$
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https://www.youtube.com/watch?v=9YgOmJdom6o
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e to the a equals m
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$e^\mathrm{a} = m$
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https://www.youtube.com/watch?v=9YgOmJdom6o
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a is equal to natural log of m
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$a=\ln m$
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https://www.youtube.com/watch?v=9YgOmJdom6o
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natural log of e to the a plus b
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$\ln(e^{a+b})$
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https://www.youtube.com/watch?v=9YgOmJdom6o
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natural log of e to the x is x
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$\ln(e^{x}) = x$
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https://www.youtube.com/watch?v=9YgOmJdom6o
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1 half natural log x plus 1 half
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$\frac{1}{2}\ln x + \frac{1}{2}$
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https://www.youtube.com/watch?v=9YgOmJdom6o
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1 over 2x plus 1 over 2 times x plus 4
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$\frac{1}{2x} + \frac{1}{2(x + 4)}$
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https://www.youtube.com/watch?v=9YgOmJdom6o
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e to the x plus e to the minus x
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$e^{x} + e^{-x}$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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1 plus x squared
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$1 + x^2$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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1 plus 1 over 2
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$1 + \frac{1}{2}$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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e to the x minus e to the minus x over 2
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$e^{x} - e^{-x} \over 2$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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x squared plus y squared equals 1
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$x^{2} + y^{2} = 1$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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x squared minus y squared
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$x^{2} - y^{2}$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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cosh squared u
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$\cosh^{2}u$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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e to the u plus e to the minus u over 2 quantity squared
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$(\frac{e^{u} + e^{-u}}{2})^2$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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e to the u minus e to the minus u over 2 quantity squared
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$( \frac {e^{u} - e^{-u}} {2} )^2$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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2 times e to the u times e to the minus u
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$2 e^{u}e^{-u}$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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2 plus e to the minus 2u minus e to the 2u minus 2
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$2 + e^{-2u} - e^{2u} - 2$
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https://www.youtube.com/watch?v=er_tQOBgo-I
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w of x plus one
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$\displaystyle w(x) + 1$
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https://www.youtube.com/watch?v=8gGbViZjoRw
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w of x plus 2 times e to the w of x
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$w(x) + 2e^{w(x)}$
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https://www.youtube.com/watch?v=8gGbViZjoRw
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1 over w of x plus 2 times e to the w of x
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$\frac{1}{w(x)} + 2e^{w(x)}$
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https://www.youtube.com/watch?v=8gGbViZjoRw
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w of one plus two times e to the w of one
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$w(1) + 2 e^{w(1)}$
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https://www.youtube.com/watch?v=8gGbViZjoRw
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1 half times x minus 1
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$\frac{1}{2}(x - 1)$
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https://www.youtube.com/watch?v=8gGbViZjoRw
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1 over x0 plus delta x
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$ \frac{1}{x_{0} +\Delta x}$
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https://www.youtube.com/watch?v=7K1sB05pE0A
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minus 1 over x0 plus delta x times x0
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$\displaystyle-\frac{1}{x_{0} + \Delta x x_{0}}$
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https://www.youtube.com/watch?v=7K1sB05pE0A
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minus 1 over 3 plus delta x times 3
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$-\frac{1}{3} + \Delta x \times 3$
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https://www.youtube.com/watch?v=7K1sB05pE0A
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minus 1 over x0 squared x minus x0
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$-\frac{1}{x_{0}^{2}}(x-x_{0})$
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https://www.youtube.com/watch?v=7K1sB05pE0A
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delta f is x plus delta x to the n minus x to the n divided by delta x
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$\displaystyle \Delta f = \frac{(x + \Delta x)^{n} - x^{n}}{\Delta x}$
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https://www.youtube.com/watch?v=7K1sB05pE0A
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x to the n plus n x to the n minus 1 delta x
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$x^{n}+nx^{n-1}\Delta x$
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https://www.youtube.com/watch?v=7K1sB05pE0A
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n x to the n minus one
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$nx^{n-1}$
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https://www.youtube.com/watch?v=7K1sB05pE0A
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minus 1 over x squared
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$-\frac{1}{x^{2}}$
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https://www.youtube.com/watch?v=ryLdyDrBfvI
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x plus 3 over x squared plus 1
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$\frac{x + 3}{x^{2} + 1}$
|
https://www.youtube.com/watch?v=ryLdyDrBfvI
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4 plus 3 divided by 4 squared plus 1
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$\frac{4+3}{4^{2}+1}$
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https://www.youtube.com/watch?v=ryLdyDrBfvI
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1 minus cosine x over x
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$\frac{1 - \cos x}{x}$
|
https://www.youtube.com/watch?v=ryLdyDrBfvI
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