Question

Find the first partial derivative $\displaystyle{\frac{\partial z}{ \partial x}}$ ​ of the function $z=x^2e^{-y}$ at point  (2,-1)

Answer 1

$\frac{\partial z}{\partial x}=2xe^{-y}$

$\frac{\partial z}{\partial x}|_{(2,-1)}=2\cdot2e^{-1}=4/e$