# Thread: partial second derivative multiple variables

1. ## partial second derivative multiple variables

I can't find the solution to this problem:
is says z=f(x,y) with x= 2s +3t and y=3s-2t. i have to find zss and zst.
Do i have to use chain rule or something else?
thanks

2. Originally Posted by benoitpouliot5757
I can't find the solution to this problem:
is says z=f(x,y) with x= 2s +3t and y=3s-2t. i have to find zss and zst.
Do i have to use chain rule or something else?
thanks

First, this is not a problem in differential equations and really belongs in the "Calculus" section. In any case, yes, you use the chain rule:
$\displaystyle \frac{\partial z}{\partial s}= \frac{\partial z}{\partial x}\frac{\partial x}{\partial s}+ \frac{\partial z}{\partial y}\frac{\partial y}{\partial s}$.

Then, of course, to get the second derivatives, do it again.

3. i know i to get xs and ys but how do i get the zx and zy. The answer of the problem is : zss=4f11 + 12f12 + 9f22. i don't understand why there are 3 terms.