audio audioduration (s) 0.83 21 | transcription stringlengths 3 127 | LaTeX stringlengths 7 142 | Source stringclasses 89
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df equals f sub x dx plus f sub y dy plus f sub z dz | $df=f_{x}dx+f_{y}dy+f_{z}dz$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
partial f partial x dx plus partial f partial y dy plus partial f over partial z dz | $\displaystyle \frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy+\frac{\partial f}{\partial z}dz$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
delta y plus fz delta z | $\displaystyle \Delta y+f(z)\Delta z$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
df dt equals f sub x dx dt plus f sub y dy dt plus f sub z dz dt | $\frac{df}{dt}=f_{x}\frac{dx}{dt}+f_{y}\frac{dy}{dt}+f_{z}\frac{dz}{dt}$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
df is f sub x dx plus f sub y dy plus f sub z dz | $\displaystyle df = f_{x}dx+f_{y}dy+f_{z}dz$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
f sub x times x prime of t dt | $f_{x}x^{\prime}(t)dt$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
f sub z z prime of t dt | $f_{z}z^{\prime}(t)dt$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
x squared y plus z | $\mathsf{x}^{2}y+z$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
w sub y is x squared times dy dt | $w_{y}={x}^2\frac{dy}{dt}$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
2t e to the t plus t squared e to the t plus cosine t | $2te^{t}+t^{2}e^{t}+\cos t$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
derivative of t squared is 2t | $\displaystyle \frac{d}{dt}t^{2}=2 t$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
t squared times the derivative of e to the t | $\displaystyle t^{2}\cdot \frac{d}{dt}{e}^{t}$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
one over v times du dt | $\displaystyle \frac{1}{v}\frac{du}{dt}$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
minus u over v squared times dv dt | $-\frac{u}{v^{2}}\frac{dv}{dt}$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
x sub u times du plus x sub v times dv | $x_{u}du+x_{v}dv$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
dy is y sub u du plus y sub v dv | $\displaystyle \mathrm{d}y\,\ =y_u \mathrm{d}u + y_{v}\,\mathrm{d}v$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
f sub x times x sub u plus f sub y times y sub u | $\displaystyle f_{x}x_{u}+f_{y}y_{u}$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
f sub x times cosine theta plus f sub y times sine theta | $f_{x}\cdot\cos \theta+f_{y}\cdot\sin \theta$ | https://www.youtube.com/watch?v=7eZVshlT33Q | |
a one x plus a two y plus a three z equals c | $a_1x+a_2y+a_3z=c$ | https://www.youtube.com/watch?v=2XraaWefBd8 | |
x squared plus y squared minus z squared equals four | $x^{2}+y^{2}-z^{2}=4$ | https://www.youtube.com/watch?v=2XraaWefBd8 | |
4x plus 2y minus 2z | $4x+2y-2z$ | https://www.youtube.com/watch?v=2XraaWefBd8 | |
two delta y minus two delta z equals zero | $2\Delta y-2\Delta z= $ | https://www.youtube.com/watch?v=2XraaWefBd8 | |
x minus two | $\displaystyle x-2$ | https://www.youtube.com/watch?v=2XraaWefBd8 | |
two times y minus one minus two times z minus one equals zero | $2(y-1)-2(z-1)=0$ | https://www.youtube.com/watch?v=2XraaWefBd8 | |
y of s equals y0 plus b times s | $y(s)=y_{0}+bs$ | https://www.youtube.com/watch?v=2XraaWefBd8 | |
gradient w dot u | $\nabla w \cdot \mathbf{u}$ | https://www.youtube.com/watch?v=2XraaWefBd8 | |
PV equals nRT | $\mathrm{PV}=\mathrm{nRT}$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
square root of x squared plus y squared | $\sqrt{x^{2}+y^{2}}$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
f sub z equals lambda g sub z | $f_{z}=\lambda g_{z}$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
f sub y equals lambda g sub y | $f_{y}=\lambda g_{y}$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
f sub y is 2y | $f_{y}=2{y}$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
g sub y is x | $g_{y}=x$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
g equals c | $g = c$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
x squared plus nine over x squared | $x^{2}+\frac{9}{x^{2}}$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
2x minus lambda y equals zero | $2x-\lambda y=0$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
lambda minus two times xy equals zero | $\lambda-2xy=0$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
negative four plus lambda squared | $-4+\lambda^{2}$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
lambda squared equals four | $\lambda^{2}=4$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
lambda is plus or minus two | $\lambda=\pm2$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
x squared equals three | $\displaystyle x^{2}=3$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
one half of a1u1 | $\frac{1}{2}a_1u_1$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
partial f over partial u one | $\partial f \over \partial u_{1}$ | https://www.youtube.com/watch?v=15HVevXRsBA | |
2x dx | $2x, \mathrm{d}x$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
x equals two | $\mathcal{x}=2$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
y plus 3z squared | $y+3z^{2}$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
dz equals minus one over six times four dx plus dy | $dz=-\frac{1}{6}(4dx+dy)$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
partial z over partial x is minus four over six | $\displaystyle \frac{\partial z}{\partial x} = -\frac{4}{6}$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
dz equals minus four sixth dx | $dz=-4x^{6}dx$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
partial z over partial x is minus gx over gz | $\frac{\partial z}{\partial x} = -\frac{{g}_{x}}{{g}_{z}}$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
b is a over cosine theta | $\displaystyle \mathcal{b} = \frac{a}{\cos\theta}$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
one half of a squared tangent theta | $\frac{1}{2}a^{2}\tan\theta$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
zero equals dA equals cosine theta dB minus B sine theta d theta | $0=dA=\cos\theta dB-B\sin\theta d\theta$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
a equals one half ab sine theta | $A=\frac{1}{2}ab\sin\theta$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
one half of ab times sine theta times tangent theta plus cosine theta d theta. | $\displaystyle \frac{1}{2}ab\sin \theta\tan \theta+\cos \theta\, d\theta$ | https://www.youtube.com/watch?v=23xbkrpQuAo | |
dg is g sub x dx plus g sub y dy plus g sub z dz | $dg =g_{x}dx+g_{y}dy+g_{z}dz$ | https://www.youtube.com/watch?v=ChiM2-MV-qM | |
minus fx gz over gx plus fz | $-f_x\frac{gz}{gx}+fz$ | https://www.youtube.com/watch?v=ChiM2-MV-qM | |
minus g sub z over g sub x, plus partial f over partial z | $-\frac{g_{z}}{g_{x}}+\frac{\partial f}{\partial z}$ | https://www.youtube.com/watch?v=ChiM2-MV-qM | |
gradient F dot product with u | $\nabla F\cdot\mathbf{u}$ | https://www.youtube.com/watch?v=ChiM2-MV-qM | |
partial h partial y is less than zero | $\partial h/\partial y<0$ | https://www.youtube.com/watch?v=ChiM2-MV-qM | |
the integral of x squared is x squared times y | $\int x^{2}dx = x^{2}y$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
the integral of y squared is y cubed over three | $\int y^{2}dy=\frac{y^{3}}{3}$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
one minus x squared minus one-third | $1-x^{2}-\frac{1}{3}$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
two thirds x minus one-third x cubed | $\frac{2}{3}x-\frac{1}{3}x^{3}$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
y is square root of one minus x squared | $y=\sqrt{1-x^{2}}$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
y minus x squared y minus y cubed over three | $y-x^{2}y-\frac{y^{3}}{3}$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
root of one minus x squared minus x squared root of one minus x squared minus y minus x squared to the three halves over three | $\displaystyle \sqrt{1-x^{2}}-x^{2}\sqrt{1 - x^{2}}-\frac{(1-x^{2})^\frac{3}{2}}{3}$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
square root of one minus x squared will be cosine theta | $\sqrt{1-x^{2}}=\cos\theta$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
x squared to a three halves | $x^{3/2}$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
two thirds times the integral from zero to pi over two of cosine to the four theta d theta | $\displaystyle \frac{2}{3}\int_{0}^{\pi/2}\cos^{4}\theta d\theta$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
one plus cosine two theta over two | $\frac{1+ \cos{(2\theta)}}{2}$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
one quarter plus one half cosine two theta plus one quarter cosine squared two theta | $\displaystyle 1/4+1/2\cos2\theta+1/4\cos^{2}2\theta$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
integral from zero to one of integral from x to square root of x of e to the y over y dy dx | $\displaystyle \int_{0}^{1}\int_{x}^{\sqrt{x}}\frac{e^{y}}{y}dydx$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
integral from zero to one of e to the y minus y e to the y dy | $\int_{0}^{1}e^{y}-ye^{y}dy$ | https://www.youtube.com/watch?v=YP_B0AapU0c | |
r minus r cubed | $(r-r^{3})$ | https://www.youtube.com/watch?v=60e4hdCi1D4 | |
one-half mr squared omega squared | $\frac{1}{2}mr^{2}\omega^{2}$ | https://www.youtube.com/watch?v=60e4hdCi1D4 | |
x squared plus y squared | $x^{2}+y^{2}$ | https://www.youtube.com/watch?v=60e4hdCi1D4 | |
pi a to the 4 over 2 | $\frac{\pi a^{4}}{2}$ | https://www.youtube.com/watch?v=60e4hdCi1D4 | |
r equals 2a cosine theta | $r=2a\cos\theta$ | https://www.youtube.com/watch?v=60e4hdCi1D4 | |
4a to the four cosine to the four theta | $4a^{4}\cos^{4}\theta$ | https://www.youtube.com/watch?v=60e4hdCi1D4 | |
three halves of pi a to the fourth | $\frac{3}{2}(\pi a^{4})$ | https://www.youtube.com/watch?v=60e4hdCi1D4 | |
x over a squared plus y over b squared equals one | $x/a^{2}+y/b^{2}=1$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
u squared plus v squared less than 1 | $u^{2}+v^{2}<1$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
u equals x over a | $u = \frac{\mathcal{x}}{\mathcal{a}}$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
du is one over a dx | $\mathrm{d}u = \frac{1}{a}\mathrm{d}x$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
dv is one over b dy | $\displaystyle dv = \frac{1}{b} \,dy$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
du dv is one over ab dx dy | $\mathrm{d}u\mathrm{d}v= \frac{1}{ab}\mathrm{d}x\mathrm{d}y$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
u equals 3x minus 2y | $u=3x-2y,$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
v equals x plus y | $\displaystyle v=x+y$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
v sub x delta x plus v sub y delta y | $v_{x}\Delta x+v_{y}\Delta y$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
x equals r cosine theta | $x=r\cos\theta$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
r cosine squared theta plus r sine squared theta | $r\cos^{2}\theta+r\sin^{2}\theta$ | https://www.youtube.com/watch?v=UZb9hZIAvL4 | |
y equals t squared | $y=t^{2}.$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
the integral along C of F dot dr | $\int_{C}\mathbf{F}\cdot d\mathbf{r}$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
negative t squared plus 2t squared | $-t^{2}+2t^{2}$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
integral from zero to one of t squared dt | $\int_{0}^{1}t^{2}dt$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
dr dt times dt | $\frac{dr}{dt}\times dt$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
M dx plus N dy | $M\,dx+N\,dy$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
negative y is minus t squared | $ -y=-t^{2}$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
dy equals 2x dx. | $dy=2xdx$ | https://www.youtube.com/watch?v=xrypSZU8cBE | |
y equals sine squared theta | $y=\sin^{2}\theta$ | https://www.youtube.com/watch?v=xrypSZU8cBE |
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