# Math Help - Partial Derivative of x^y

1. ## Partial Derivative of x^y

For $f(x,y) = x^2cos(y) - \frac{x^3}{y^2} + x^y$

Find..... $f_x, f_y, f_x_x, f_y_y, f_x_y, f_y_x$

I know how to do this expect i am running into trouble with the $x^y$ term.

so the x partial derivative ( $f_x$) of $x^y$ is .... $x^yln(x)$ ????

and the y partial derivative ( $f_y$) of $x^y$ is .... $x$ ????

Thank you

2. When you are finding $f_x$, you treat $y$ as a constant.

So $\frac{\partial}{\partial x}(x^y) = x^{y-1}y$.

When you are finding $f_y$, you treat $x$ as a constant.

So $\frac{\partial}{\partial y}(x^y) = x^y\ln{x}$.

3. Perfect that is exactly what i needed

Thank you so much!