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one over n cubed
$\frac{1}{n^{3}}$
https://www.youtube.com/watch?v=MK_0QHbUnIA
1 over n cubed.
\frac{1}{n^{3}}
one plus one over two plus all the way up to one over n minus one plus 1 over n
$1+\frac{1}{2}+\mathrm{\ldots}+\frac{1}{n-1}+\frac{1}{n}$
https://www.youtube.com/watch?v=MK_0QHbUnIA
1 1 2 all the way up to 1 n 1 1 n.
1+\frac{1}{2}+\mathrm\ldots+\frac{1}{n-1}+\frac{1}{n}
a half plus a third
$\frac{1}{2}+\frac{1}{3}$
https://www.youtube.com/watch?v=MK_0QHbUnIA
A half plus a third.
\frac{1}{2}+\frac{1}{3}
1 over n squared plus 1 square root
$\frac{1}{n^{2} + 1}$
https://www.youtube.com/watch?v=MK_0QHbUnIA
1 over n2 plus 1 square root.
\frac{1}{n^{2}+1}
sum one over n to the five-halves
$\sum\frac{1}{n^{5/2}}$
https://www.youtube.com/watch?v=MK_0QHbUnIA
Sum 1 over n to the 5 halves.
\sum\frac{1}{n^{5/2}}
one times one plus two times minus two plus minus three times one
$1\times1+2\times(-2)+(-3)\times1$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
1 times 1 plus 2 times minus 2 plus minus 3 times 1.
1\times\\1+2\times(-2)+(-3)\times\\1
x plus 3y plus z equals zero
$x+3y+z=0$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
x plus 3y plus z equals 0
x+3y+z=0
minus 2x minus z will be x plus 3y plus z
$-2x-z\operatorname{=}x+3y+z$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
minus 2x minus z will be x plus three y plus z.
-2x-z\operatorname{=}x+3y+z
x equals minus 3t
$x=-3t$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
x equals minus three t.
x=-3t
y equals 3t
$y=3\mathfrak{t}$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
y equals 3t.
y=3\mathfrak\\t
z equals negative 6t
$z\!=\!-6t$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
z equals negative 60.
z\!=\!\\-6t
dr dt dot r plus r dot dr dt
$\displaystyle \frac{dr}{dt}\cdot{r}+r\cdot\frac{dr}{dt}$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
dR by dt dot r plus r dot dR by dt.
\frac{dr}{dt}\cdot{r}+r\cdot\frac{dr}{dt}
d by dt of r dot r is zero
$\displaystyle \frac{d}{dt}(\mathbf{r}\cdot\mathbf{r})=0$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
d by dt of r dot r is zero.
\frac{d}{dt}(\mathbf\\r\cdot\mathbf\\r)=0
minus v dot v
$-\mathbf{v}\cdot\mathbf{v}$
https://www.youtube.com/watch?v=U1EcnfTKXJ0
minus v dot v
-\mathbf\\v\cdot\mathbf\\v
f of x y equals one over x plus y
$f(x,y)=\frac{1}{x+y}$
https://www.youtube.com/watch?v=dK3NEf13nPc
f of x, y equals one over x plus y.
f(x,y)=\frac{1}{x+y}
f of x y equals one minus x squared minus y squared
$f(x,y)=1-x^{2}-y^{2}$
https://www.youtube.com/watch?v=dK3NEf13nPc
f equals one minus x squared minus y squared.
f(x,y)=1-x^{2}-y^{2}
z equals one minus x squared minus y squared
$z=1-x^{2}-y^{2}$
https://www.youtube.com/watch?v=dK3NEf13nPc
z equals one minus x square minus y square.
z=1-x^{2}-y^{2}
x squared plus y squared equals one
$x^{2}+y^{2}=1$
https://www.youtube.com/watch?v=dK3NEf13nPc
x squared plus y squared equals 1.
x^{2}+y^{2}=1
f prime at x0 times delta x
$ f^{\prime}(x_{0})\Delta x$
https://www.youtube.com/watch?v=dK3NEf13nPc
f prime at x0 times delta x.
f^{\prime}(x_{0})\Delta\\x
d dy of y to the n times dy dx
$\displaystyle (\frac{d}{dy}y^{n})\frac{dy}{dx}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
dy dx.
(\frac{d}{dy}y^{n})\frac{dy}{dx}
m x to the n minus one
$(mx^{m-1})$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
m x to the m minus 1.
(mx^{m-1})
n y to the n minus 1
$(ny^{n-1})$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
Ny to the n-1.
(ny^{n-1})
x to the m minus one
$\mathcal{x}^{m-1}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
x to the m minus 1.
\mathcal\\x^{m-1}
x to the m over n times n minus 1
$x^\frac{m}{n}{(n-1)}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
x to the m over n times n-1.
x^{\frac{m}{n}}{(n-1)}
minus one plus m over n
$-1+\frac{m}{n}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
Minus 1 plus m over n.
-1+\frac{m}{n}
a minus one
$\mathsf{a}-1$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
a minus 1.
\mathsf\\a-1
a x to the a minus one
$(ax^{a-1})$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
a x to the a minus 1.
(ax^{a-1})
y is equal to plus or minus square root of 1 minus x squared
$y =\pm\sqrt{1-x^{2}}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
y is equal to plus or minus square root of 1 minus x squared.
y=\pm\sqrt{1-x^{2}}
2 x plus 2 y y prime
$2x+2yy^{\prime}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
2x plus 2yy prime.
2x+2yy^{\prime}
y to the fourth plus xy squared minus two is equal to zero
$y^{4}+xy^{2}-2=0$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
So y to the fourth plus xy squared minus 2 is equal to 0.
y^{4}+xy^{2}-2=0
four y cubed y prime
$4y^{3}y^{\prime}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
4y cubed y prime.
4y^{3}y^{\prime}
minus y squared divided by 4y cubed plus 2xy
$-\frac{y^{2}}{4y^{3}+2xy}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
Minus y squared divided by 4y cubed plus 2xy.
-\frac{y^{2}}{4y^{3}+2xy}
y to the fourth plus xy squared minus 2 is equal to zero
$y^{4}+xy^{2}-2=0$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
y to the fourth plus xy squared minus two is equal to zero.
y^{4}+xy^{2}-2=0
minus 1 squared divided by 4 times 1 cubed plus 2 times 1 times 1
$\frac{(-1)^2}{4\times1^{3}+2\times1\times1}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
Minus 1 squared divided by 4 times 1 cubed plus 2 times 1 times 1.
\frac{(-1)^{2}}{4\times\\1^{3}+2\times\\1\times\\1}
tan inverse x is equal to pi over two
$\operatorname{\tan}^{-1}x=\frac{\pi}{2}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
tan inverse x is equal to pi over 2.
\operatorname{\tan}^{-1}x=\frac{\pi}{2}
d by dy tan y times dy dx
$\displaystyle \frac{d}{dy}\tan(y)\frac{dy}{dx}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
d by dy tan y times dy dx.
\frac{d}{dy}\tan(y)\frac{dy}{dx}
d by dx of tan inverse of x
$\frac{d}{dx}(tan^{-1}(x))$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
d by dx of tan inverse of x.
\frac{d}{dx}(tan^{-1}(x))
cosine squared of tan inverse x
$\cos^{2}(tan^{-1}x)$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
Cosine squared of tan inverse x.
\cos^{2}(tan^{-1}x)
one over 1 plus x squared
$\frac{1}{1+x^{2}}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
1 over 1 plus x squared.
\frac{1}{1+x^{2}}
d by dx of tan inverse x is equal to one over 1 plus x squared
$\frac{d}{dx}(tan^{-1}x)=\frac{1}{1 + x^{2}}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
d by dx of tan inverse x is equal to 1 over 1 plus x squared.
\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}}
1 over square root of 1 minus x squared
$\frac{1}{\sqrt{1-x^{2}}}$
https://www.youtube.com/watch?v=5q_3FDOkVRQ
1 over square root of 1 minus x squared.
\frac{1}{\sqrt{1-x^{2}}}
a to the x1 plus x2 is a to the x1 times a to the x2
$\displaystyle a^{x_1 + x_2} = a^{x_{1}}\cdot a^{x_{2}}$
https://www.youtube.com/watch?v=9v25gg2qJYE
a to the x1 plus x2 is a to the x1 times a to the x2.
a^{x_{1}+x_{2}}=a^{x_{1}}\cdot\\a^{x_{2}}
a to the x plus delta x
$a^{x+\Delta x}$
https://www.youtube.com/watch?v=9v25gg2qJYE
a to the x plus delta x.
a^{x+\Delta\\x}
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
$M(a)=\lim_{\Delta x\to 0}\frac{a^{\Delta x}-1}{\Delta x}$
https://www.youtube.com/watch?v=9v25gg2qJYE
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.
M(a)=\lim_{\Delta\\x\to\\0}\frac{a^{\Delta\\x}-1}{\Delta\\x}
k times f prime of kx
$k\cdot f^{\prime}(kx)$
https://www.youtube.com/watch?v=9v25gg2qJYE
K times f prime of kx.
k\cdot\\f^{\prime}(kx)
e to the log x is equal to x
$\mathrm{e}^{\log x}=x$
https://www.youtube.com/watch?v=9v25gg2qJYE
E to the log x is equal to x.
\mathrm\\e^{\log\\x}=x
d by dx e to the w
$\frac{d}{dx}\mathbf{e}^{w}$
https://www.youtube.com/watch?v=9v25gg2qJYE
D by dx, e to the w.
\frac{d}{dx}\mathbf\\e^{w}
e to the power log a to the power x
$(e^{\ln a})^{x}$
https://www.youtube.com/watch?v=9v25gg2qJYE
e to the power log a to the power x.
(e^{\ln\\a})^{x}
d by dx of a to the x is equal to d by dx of e to the x log a
$\frac{d}{dx}(a^{x})=\frac{d}{dx}(e^{x}\log a)$
https://www.youtube.com/watch?v=9v25gg2qJYE
d by dx of a to the x is equal to d by dx of e to the x log a.
\frac{d}{dx}(a^{x})=\frac{d}{dx}(e^{x}\log\\a)
log a times e to the x log a
$\log a\,\mathrm{e}^{x\log a}$
https://www.youtube.com/watch?v=9v25gg2qJYE
log A times e to the x log A.
\log\\a\,\mathrm\\e^{x\log\\a}
The derivative with respect to x of 2 to the x is log 2 times 2 to the x
$\frac{d}{dx}(2^{x})=\log{2}(2^{x})$
https://www.youtube.com/watch?v=9v25gg2qJYE
The derivative with respect to x of 2 to the x is log 2 times 2 to the x.
\frac{d}{dx}(2^{x})=\log{2}(2^{x})
log 10 times 10 to the x
$\log 10\times 10^{x}$
https://www.youtube.com/watch?v=9v25gg2qJYE
log 10 times 10 to the x.
\log\\10\times\\10^{x}
log u prime is equal to u primie over u
$\log u^{\prime}=u^{\prime}/u$
https://www.youtube.com/watch?v=9v25gg2qJYE
Log u' is equal to u' over u.
\log\\u^{\prime}=u^{\prime}/u
u prime is equal to u times log a
$u^{\prime}=u\cdot\log a$
https://www.youtube.com/watch?v=9v25gg2qJYE
u' is equal to u log a.
u^{\prime}=u\cdot\log\\a
v prime is equal to v times 1 plus log x
$v^{\prime}=v(1+\log x)$
https://www.youtube.com/watch?v=9v25gg2qJYE
v' is equal to v times 1 plus log x.
v^{\prime}=v(1+\log\\x)
d by dx x to the x
$(\frac{d}{dx}(x^{x}))$
https://www.youtube.com/watch?v=9v25gg2qJYE
d by dx, x to the x.
(\frac{d}{dx}(x^{x}))
one plus one over n to the power n
$(1+\frac{1}{n})^{n}$
https://www.youtube.com/watch?v=9v25gg2qJYE
1 plus 1 over n to the power n.
(1+\frac{1}{n})^{n}
n log one plus one over n
$n\log(1+1/n)$
https://www.youtube.com/watch?v=9v25gg2qJYE
n log 1 plus 1 over n.
n\log(1+1/n)
one plus one over k to the kth power
$(1+\frac{1}{k})^{k}$
https://www.youtube.com/watch?v=eHJuAByQf5A
1 plus 1 over k to the kth power.
(1+\frac{1}{k})^{k}
ln of one plus one over k
$\ln(1+\frac{1}{k})$
https://www.youtube.com/watch?v=eHJuAByQf5A
Allen of 1 plus 1 over K.
\ln(1+\frac{1}{k})
e to the r log x prime
$\mathrm{e}^{r}\log x^{\prime}$
https://www.youtube.com/watch?v=eHJuAByQf5A
e to the r log x prime.
\mathrm\\e^{r}\log\\x^{\prime}
u times r divided by x
$u\times\mathbb{r}/x$
https://www.youtube.com/watch?v=eHJuAByQf5A
U times R divided by X.
u\times\mathbb\\r/x
r x to the r minus one
$rx^{r-1}$
https://www.youtube.com/watch?v=eHJuAByQf5A
R, x to the r minus 1.
rx^{r-1}
y is ten x plus b
$y=10x+b$
https://www.youtube.com/watch?v=eHJuAByQf5A
y is 10x plus b.
y=10x+b
fifty t plus ten a plus b
$50t+10a+b$
https://www.youtube.com/watch?v=eHJuAByQf5A
50 T plus 10 A plus B.
50t+10a+b
minus v to the minus 2 times v prime
$-v^{-2}v^{\prime}$
https://www.youtube.com/watch?v=eHJuAByQf5A
Minus v to the minus 2 times v prime.
-v^{-2}v^{\prime}
x to the ten plus eight x
$x^{10}+8x$
https://www.youtube.com/watch?v=eHJuAByQf5A
x to the 10th plus 8x.
x^{10}+8x
e to the x tan inverse x
$\mathrm{e}^{x}{\tan^{-1}x}$
https://www.youtube.com/watch?v=eHJuAByQf5A
e to the x tan inverse x.
\mathrm\\e^{x}{\tan^{-1}x}
x divided by 1 plus x squared
$\frac{x}{1+x^{2}}$
https://www.youtube.com/watch?v=eHJuAByQf5A
x divided by 1 plus x squared.
\frac{x}{1+x^{2}}
the limit as delta x goes to 0 of f of x plus delta x minus f of x divided by delta x
$\displaystyle \lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$
https://www.youtube.com/watch?v=eHJuAByQf5A
The limit as delta x goes to 0 of f of x plus delta x minus f of x divided by delta x.
\lim_{\Delta\\x\to\\0}\frac{f(x+\Delta\\x)-f(x)}{\Delta\\x}
one over one plus y squared times y prime
$\frac{1}{1+y^{2}}y^{\prime}$
https://www.youtube.com/watch?v=eHJuAByQf5A
1 over 1 plus y squared times y prime.
\frac{1}{1+y^{2}}y^{\prime}
one divided by the square root of one plus x squared
$1/\sqrt{1+x^{2}}$
https://www.youtube.com/watch?v=eHJuAByQf5A
1 divided by the square root of 1 plus x squared.
1/\sqrt{1+x^{2}}
x zero plus f prime of x zero x minus x zero
$\displaystyle x_{0}+f^{\prime}(x_{0})(x - x_{0})$
https://www.youtube.com/watch?v=BSAA0akmPEU
X0 plus f prime of X0, X minus X0.
x_{0}+f^{\prime}(x_{0})(x-x_{0})
y equals cosine x
$y=\cos x$
https://www.youtube.com/watch?v=BSAA0akmPEU
y equals cosine x.
y=\cos\\x
y equals e to the x
$y=\mathrm{e}^{x}$
https://www.youtube.com/watch?v=BSAA0akmPEU
Y equals e to the x.
y=\mathrm\\e^{x}
y equals one plus x
$\displaystyle y=1+x$
https://www.youtube.com/watch?v=BSAA0akmPEU
y equals 1 plus x
y=1+x
f prime is one over one plus x
$f^{\prime}=\frac{1}{1+x}$
https://www.youtube.com/watch?v=BSAA0akmPEU
f prime is 1 over 1 plus x.
f^{\prime}=\frac{1}{1+x}
r one plus x to the r minus 1
$(r\cdot{1+x}^{r-1})$
https://www.youtube.com/watch?v=BSAA0akmPEU
R 1 plus x to the r minus 1.
(r\cdot{1+x}^{r-1})
e to the minus 3x divided by square root 1 plus x
$e^{-3x}/\sqrt{1+x}$
https://www.youtube.com/watch?v=BSAA0akmPEU
E to the minus 3x divided by square root 1 plus x.
e^{-3x}/\sqrt{1+x}
e to the minus three x one plus x to the minus a half
$e^{-3x}(1+x^{-1/2})$
https://www.youtube.com/watch?v=BSAA0akmPEU
e to the minus 3x, 1 plus x to the minus 1 half.
e^{-3x}(1+x^{-1/2})
one minus three x minus a half of x plus three halves x squared.
$1-3x-\frac{1}{2}x+\frac{3}{2}x^{2}$
https://www.youtube.com/watch?v=BSAA0akmPEU
1 minus 3x minus 1 half x plus 3 halves x squared.
1-3x-\frac{1}{2}x+\frac{3}{2}x^{2}
t prime is equal to t divided by the square root of 1 minus v squared over c squared
$t^{\prime}= t/\sqrt{1-v^{2}/c^{2}}$
https://www.youtube.com/watch?v=BSAA0akmPEU
T prime is equal to T divided by the square root of 1 minus V squared over C squared.
t^{\prime}=t/\sqrt{1-v^{2}/c^{2}}
v squared over c squared
$\frac{v^{2}}{c^{2}}$
https://www.youtube.com/watch?v=BSAA0akmPEU
V squared over C squared.
\frac{v^{2}}{c^{2}}
t times 1 plus a half v squared over c squared
$t(1+\frac{1}{2}\frac{v^{2}}{c^{2}})$
https://www.youtube.com/watch?v=BSAA0akmPEU
T times 1 plus 1 half v squared over c squared.
t(1+\frac{1}{2}\frac{v^{2}}{c^{2}})
y equals one minus a half x squared
$y=1-\frac{1}{2}x^{2}$
https://www.youtube.com/watch?v=BSAA0akmPEU
y equals 1 minus 1 half x squared.
y=1-\frac{1}{2}x^{2}
one plus a half v squared over c squared
$1+\frac{1}{2}v^{2}/c^{2}$
https://www.youtube.com/watch?v=eRCN3daFCmU
1 plus 1 half v squared over c squared.
1+\frac{1}{2}v^{2}/c^{2}
f double prime of zero divided by two
$f^{\prime\prime}(0)/2$
https://www.youtube.com/watch?v=eRCN3daFCmU
f double prime of 0 divided by 2.
f^{\prime\prime}(0)/2
sine x is approximately x
$\sin x\approx x$
https://www.youtube.com/watch?v=eRCN3daFCmU
Sine x is approximately x.
\sin\\x\approx\\x
cosine x is approximately one minus a half x squared
$\cos x\approx 1-\frac{1}{2}x^{2}$
https://www.youtube.com/watch?v=eRCN3daFCmU
Cosine x is approximately 1 minus 1 half x squared.
\cos\\x\approx\\1-\frac{1}{2}x^{2}
e to the x is approximately one plus x plus a half x squared
$e^{x}\approx 1+x+\frac{1}{2}x^{2}$
https://www.youtube.com/watch?v=eRCN3daFCmU
e to the x is approximately 1 plus x plus 1 half x squared.
e^{x}\approx\\1+x+\frac{1}{2}x^{2}
x minus a half x squared
$x-\frac{1}{2}x^{2}$
https://www.youtube.com/watch?v=eRCN3daFCmU
x minus 1 half x squared
x-\frac{1}{2}x^{2}
1 plus x to the power r
$(1+x^{r})$
https://www.youtube.com/watch?v=eRCN3daFCmU
1 plus x to the power r.
(1+x^{r})
one plus rx plus r times r minus one divided by two x squared
$1+rx+\frac{r(r-1)}{2}x^{2}$
https://www.youtube.com/watch?v=eRCN3daFCmU
1 plus rx plus r times r minus 1 divided by 2x squared.
1+rx+\frac{r(r-1)}{2}x^{2}
e to the minus three x one plus x to the minus a half
$e^{-3x}(1+x)^{-1/2}$
https://www.youtube.com/watch?v=eRCN3daFCmU
e to the minus 3x, 1 plus x to the minus 1 half.
e^{-3x}(1+x)^{-1/2}
one minus a half x plus a half times minus a half times minus three halves x squared
$1-\frac{1}{2}x+\frac{1}{2}\times(-\frac{1}{2})\times(-\frac{3}{2})x^{2}$
https://www.youtube.com/watch?v=eRCN3daFCmU
1 minus 1 half x plus 1 half times minus 1 half times minus 3 halves x squared.
1-\frac{1}{2}x+\frac{1}{2}\times(-\frac{1}{2})\times(-\frac{3}{2})x^{2}
f double prime is minus one over one plus x squared
$f^{\prime\prime}=-\frac{1}{1 + x^{2}}$
https://www.youtube.com/watch?v=eRCN3daFCmU
f double prime is minus 1 over 1 plus x squared.
f^{\prime\prime}=-\frac{1}{1+x^{2}}
r one plus x to the r minus one
$(r\cdot 1+x^{r-1})$
https://www.youtube.com/watch?v=eRCN3daFCmU
r 1 plus x to the r minus 1.
(r\cdot\\1+x^{r-1})
r times r minus one x plus one to the r minus two
$r(r-1)(x+1)^{r-2}$
https://www.youtube.com/watch?v=eRCN3daFCmU
r times r minus 1, x plus 1 to the r minus 2.
r(r-1)(x+1)^{r-2}
3 times 1 minus x times 1 plus x
$3(1-x)(1+x)$
https://www.youtube.com/watch?v=eRCN3daFCmU
3 times 1 minus x times 1 plus x.
3(1-x)(1+x)
one minus x times 1 plus x is zero
$(1 - x)(1 + x) = 0$
https://www.youtube.com/watch?v=eRCN3daFCmU
1 minus x times 1 plus x is 0.
(1-x)(1+x)=0