What steps do I need to follow to get the partial derivative with respect to $x$ and separately with respect to $y$ for the following function (I can't seem to get to the correct solution):
$$f(x,y) = e^{-x} + e^{-2y}$$
Thanks in advance for any help.
With respect to $x$, $e^{-2y}$ is constant and its derivative is $0$, so the partial derivative with respect to $x$ is just the derivative of $e^{-x}$ which is $-e^{-x}$.
With respect to $y$, $e^{-x}$ is constant and its derivative is $0$, so the partial derivative with respect to $y$ is just the derivative of $e^{-2y}$ which is $-2e^{-2y}$.