# Thread: Multivariable/generalized chain rule -- Need help!

1. ## Multivariable/generalized chain rule -- Need help!

I know how to apply the generalized chain rule for functions of this type:
z=u^2+v^2, u=x^2y and v=xy
∂z/∂u=∂z/∂u * ∂u/∂x+∂z/∂v * ∂v/∂x etc.

I came across a function of this type:
z=f(u,v), u=x^2y^2 and v=5x+1
Because of the f(u,v), I don't know how to proceed! Anyone could give me a hint on how to find partial derivatives of this function? What is it that I don't understand?

Thanks!

2. ## Re: Multivariable/generalized chain rule -- Need help!

Hey tweakedsam.

What kind of derivative are you trying to find? Can you give an example?

3. ## Re: Multivariable/generalized chain rule -- Need help!

I don't understand how the second situation is different from the first. In both cases z depends on u and v, u depends on x and y, and v depends on x and y.

Is it because you have to leave $\frac{\partial{z}}{\partial{u}}$ as just $\frac{\partial{f}}{\partial{u}}$? You can't calculate it any further without knowing more about f, right?

- Hollywood