# Thread: Help deriving this function

1. ## Help deriving this function

I need to find the stationary point, but I'm unsure the partial derivatives.

$f(x)=e^{-x^2-y^2}$

Any help will be appreciated

2. $f(x)=e^{-x^2-y^2}$

With respect to x hold y constant and vice versa. Consider when $y= e^{f(x)} \Rightarrow \frac{dy}{dx}= f'(x)e^{f(x)}$

so

$\frac{\partial f}{\partial x} = -2xe^{-x^2-y^2}
$

can you find

$\frac{\partial f}{\partial y}$ ?

3. It might be simpler to write $e^{-x^2-y^2}$ as $e^{-x^2}e^{-y^2}$. What is the derivative of $Ce^{-x^2}$ with respect to x?