Answer
$\frac{∂f}{∂x}=3x^{-0.4}y^{0.4}$
$\frac{∂f}{∂y}=2x^{0.6}y^{-0.6}$
$\frac{∂f}{∂x}|_{(1,-1)}=undefined$
$\frac{∂f}{∂y}|_{(1,-1)}=undefined$
Work Step by Step
$f(x,y)=5x^{0.6}y^{0.4}$
$\frac{∂f}{∂x}=5(0.6)x^{-0.4}y^{0.4}=3x^{-0.4}y^{0.4}$
$\frac{∂f}{∂y}=5x^{0.6}(0.4)y^{-0.6}=2x^{0.6}y^{-0.6}$
$\frac{∂f}{∂x}|_{(1,-1)}=3(1)^{-0.4}(-1)^{0.4}=undefined$
$\frac{∂f}{∂y}|_{(1,-1)}=2(1)^{0.6}(-1)^{-0.6}=undefined$
The last two values are undefined because $(-1)^{0.4}$ and $(-1)^{-0.6}$ are undefined.
