If there is a function $z=f(x^2 + y^2)$
What is the partial differential of $z$ w.r.t to ?
I think it is equal to the partial differential f w.r.t to $x$ multiplied by $2x$.
But the answer is wrong. It includes some total derivative which I don't understand .
First of all I want to know why is the above wrong ? What is wrong in the above chain rule application? Why do we have use the total derivative ?