1. ## Chain Rule

Hi I am stuck on this problem. Can someone please explain. Thanks!

Let
Compute
_________
_________

2. Originally Posted by jffyx
Hi I am stuck on this problem. Can someone please explain. Thanks!

Let
Compute
_________
_________
Here's a hint: by the chain rule

$\frac {\partial w}{\partial s} = \frac {\partial w}{\partial x} \cdot \frac {\partial x}{\partial s} + \frac {\partial w}{\partial y} \cdot \frac {\partial y}{\partial s} + \frac {\partial w}{\partial z} \cdot \frac {\partial z}{\partial s}$

and, similarly,

$\frac {\partial w}{\partial t} = \frac {\partial w}{\partial x} \cdot \frac {\partial x}{\partial t} + \frac {\partial w}{\partial y} \cdot \frac {\partial y}{\partial t} + \frac {\partial w}{\partial z} \cdot \frac {\partial z}{\partial t}$

(2,-1) refers to (s,t) it seems (that is, if the problem described the functions as x(s,t) for instance). you can find the corresponding x, y and z values for this point

3. I still do not understand clearly on how to do the problem. Can someone please explain. Thanks a lot.

4. Originally Posted by jffyx
I still do not understand clearly on how to do the problem. Can someone please explain. Thanks a lot.
can you find each of the partial derivatives that you see on the right side of the equations i gave you?

5. yea i can find the partials, but when i plug into the chain rule formula i get 3 variables... im stuck on that step

6. Originally Posted by jffyx
yea i can find the partials, but when i plug into the chain rule formula i get 3 variables... im stuck on that step
ok, so you found all the partials, and you plugged them into the formula. now all that's left is to plug in values for the variables. remember, $(s,t) = (-2,-1)$

hence we have $s = -2,~t = -1,~x = 2,~y = e^2, \text{ and } z = 1$

7. yay i got thanks for all the help