# Homework Help: Finding the partial derivatives of function

1. Nov 1, 2012

### chmate

1. The problem statement, all variables and given/known data

If $z=\frac{1}{x}[f(x-y)+g(x+y)]$, prove that $\frac{\partial }{\partial x}(x^2\frac{\partial z}{\partial x})=x^2\frac{\partial^2 z}{\partial y^2}$

2. Relevant equations

3. The attempt at a solution

I don't know how I'm supposed to find the partial derivative of z with respect to any of variables if the function f and g are not expressed.
Help me!

Thank you

2. Nov 1, 2012

### LCKurtz

Just leave the f and g in there, maybe they will cancel out. For example, if you want the partial of f(x-y) with respect to y it would be:$$f_y(x-y) = -1\cdot f'(x-y)$$and so on.

3. Nov 1, 2012

### chmate

Can you explain me why $f_y(x-y) = -1\cdot f'(x-y)$? I don't get it.
What is then $f_x(x+y) = ?$

4. Nov 1, 2012

### LCKurtz

It is the chain rule. If you have $z=f(x-y)$ let $u = x-y$ so $z=f(u)$. Your chain rule for is$$z_x = z_u u_x,\ z_y = f_u u_y$$and since f depends on only one variable u, you would write $f_u = f'(u)$ and you multiply by the $u_x$ or $u_y$ accordingly.