Partial Derivative/Examples/x^(x y)

Example of Partial Derivative
Let $\map f {x, y} = x^{x y}$ be a real function of $2$ variables such that $x, y \in \R_{>0}$.

Then:


 * $\dfrac {\partial f} {\partial x} = x^{x y} \paren {y \ln x + y}$


 * $\dfrac {\partial f} {\partial y} = x^{x y + 1} \ln x$