# Conflicting result in derivative of composite function

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1. Oct 10, 2016

### toforfiltum

1. The problem statement, all variables and given/known data
Let $$f(x,y)=\begin{cases} \frac{x^2y}{x^2+y^2} \space & \text{if} \space(x,y)\neq(0,0)\\0 \space & \text{if} \space(x,y)=(0,0)\end{cases}$$

a) Use the definition of the partial derivative to find $f_x(0,0)$ and $f_y(0,0)$.

b) Let a be a nonzero constant and let $x(t)=(t,at)$. Show that $f\circ x$ is differentiable, and find $D(f\circ x)(0)$ directly.