# Basic partial differentiation help (needs checking)

1. Mar 26, 2012

### niekehecv

1. The problem statement, all variables and given/known data
given z=yf(x^2-y^2)
show that the x(∂z/∂y)+y(∂z/∂x)=xz/y

3. The attempt at a solution

cut it short, my
∂z/∂y= f(x^2-y^2)-2(y^2)f(x^2-y^2)
∂z/∂x=2xyf(x^2-y^2)

i was able to prove that
x(∂z/∂y)+y(∂z/∂x)=xz/y

But i need help with partial differentiations when they give an equation like z=f(x^2-y^2)
I've read about partially differentiating such equations somewhere before. Can someone please check if i am doing it right? Also, what is this kind of partial differentiation called? (such as partially differentiating z=f(x^2-y^2)
I would really appreciate if someone could tell me what is it called so i could read up more about it and do more examples of this kind.

2. Mar 26, 2012

### LCKurtz

When you have something like $z=f(x^2-y^2)$ you need to use the chain rule. The easiest way to see this is to look at as $z = f(u),\ u=x^2-y^2$ Now if you want to calculate $z_x$ you use$$z_x = f'(u)u_x = f'(x^2-y^2)(-2x)$$You are missing the primes in your argument.

3. Mar 26, 2012