Exercises
[1G4]Are the following functions differentiable in \((0,0)\)?
\begin{align*} f_ 1(x,y)= \begin{cases} x+y & \text{if}~ x{\gt}0\\ x+ye^{-x^ 2} & \text{if}~ x≤ 0 \end{cases}& ,& f_ 2(x,y) = \sqrt{x^ 2+y^ 2} \\ f_ 3(x,y) = \left( \arctan (y+1)\right)^{x+1} & ,& f_ 4(x,y) =\max \{ x^ 2, y^ 2\} ~ ~ . \end{align*}Solution 1