# Thread: Partial Derivative - Chain Rule

1. ## Partial Derivative - Chain Rule

I have this problem which I am stuck on. It tells me to find the derivative of the function in 2 ways...first by substitution then by the chain rule using partial derivatives. I found the first one fine using substitution then taking a derivative. The second one I came up with a different answer (which I believe is incorrect). Can someone help me get unstuck please? I've attached a picture of my work. Thanks

2. ## Re: Partial Derivative - Chain Rule

I didn't check whole the answer but I notice a mistake by calculating $\frac{dz}{dy}$ with the chain rule:
$\frac{d}{dy}\left(\frac{x}{x^2+y^2}\right)=x\cdot \frac{d}{dy}(x^2+y^2)^{-1}$
$=-x\cdot(x^2+y^2)^{-2}\cdot 2y =\frac{-2xy}{(x^2+y^2)^2}$