## Calculus 8th Edition

$$\frac{\partial}{\partial x}f(x,y)=yx^{y-1}$$ $$\frac{\partial}{\partial y}f(x,y)=x^y\ln x$$
Regard $y$ as constant and differentiate with respect to $x$. Then $f$ is treated as a simpe power function: $$\frac{\partial}{\partial x}f(x,y)=\frac{\partial}{\partial x}x^y=yx^{y-1}.$$ Regard $x$ as constrant and differentiate with respect to $y$. Then $f$ is treated as a simpe exponential function: $$\frac{\partial}{\partial y}f(x,y)=\frac{\partial}{\partial y}x^y=x^y\ln x.$$