- #1

james weaver

- 27

- 4

- Homework Statement:
- show the relationship between rectangular and polar partial derivatives

- Relevant Equations:
- symbolic

Hello, I am trying to solve the following problem:

If ##z=f(x,y)##, where ##x=rcos\theta## and ##y=rsin\theta##, find ##\frac {\partial z} {\partial r}## and ##\frac {\partial z} {\partial \theta}## and show that ##\left( \frac {\partial z} {\partial x}\right){^2}+\left( \frac {\partial z} {\partial y}\right){^2}=\left( \frac {\partial z} {\partial r}\right){^2}+\frac 1 {r^2}\left( \frac {\partial z} {\partial \theta}\right){^2}##

I am a little lost on how, I know I need to use the chain rule. This is what i have so far:

##\frac {\partial z} {\partial r}=\frac {\partial z} {\partial f}\frac {\partial f} {\partial r}##

and

##\frac {\partial z} {\partial \theta}=\frac {\partial z} {\partial f}\frac {\partial f} {\partial \theta}##

So i can find them symbolically, but not sure how to explicitly. If anyone has a good video they can shoot my way I would appreciate that as well. Thanks.

If ##z=f(x,y)##, where ##x=rcos\theta## and ##y=rsin\theta##, find ##\frac {\partial z} {\partial r}## and ##\frac {\partial z} {\partial \theta}## and show that ##\left( \frac {\partial z} {\partial x}\right){^2}+\left( \frac {\partial z} {\partial y}\right){^2}=\left( \frac {\partial z} {\partial r}\right){^2}+\frac 1 {r^2}\left( \frac {\partial z} {\partial \theta}\right){^2}##

I am a little lost on how, I know I need to use the chain rule. This is what i have so far:

##\frac {\partial z} {\partial r}=\frac {\partial z} {\partial f}\frac {\partial f} {\partial r}##

and

##\frac {\partial z} {\partial \theta}=\frac {\partial z} {\partial f}\frac {\partial f} {\partial \theta}##

So i can find them symbolically, but not sure how to explicitly. If anyone has a good video they can shoot my way I would appreciate that as well. Thanks.