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