Question

Find the first partial derivatives of the function: f(x,y,z,t) = xyz^2tan(yt)

Answer 1

\[f(x,y,z,t) = xyz^2\tan(yt) \]

Answer 2

\[\frac{\partial}{\partial x} f(x,y,z,t)\\
= \frac{\partial}{\partial x}xyz^2\tan(yt)\\
= \frac{\partial}{\partial x}\big(x\big)\cdot yz^2\tan(yt)+x\cdot \frac{\partial}{\partial x}\big(yz^2\tan(yt)\big)\\=\\=\]

Answer 3

Partial Derivative in respect to x is:
\[yz^2(1)\tan(yt) => yz^2\tan(yt)\]

Answer 4

yes!

Answer 5

Cool thanks
Now I just have to do the rest of the partial derivatives for y, z and t now. But I'll think I'll take it form here!

Answer 6

the partial with respect to y is a bit trickier,

Answer 7

Oh yeah, possibly product rule ~

Answer 8

yeah, and the chain rule too

Answer 9

And that too, for that trig function part