# Thread: Higher Order Partial Derivative

1. ## Higher Order Partial Derivative

I've been struggling with this one for a while. I can't seem to get it right. I have to find fxxyy of e^(x^2+y^3)
I cannot arrive at the correct answer. A little guidance would be greatly appreciated.

2. When we find a partial derivative with respect to a variable, we differentiate normally with respect to that variable while treating all other independent variables as constants. For example, if $f(x,\,y)=x^2\sin y$, then

\begin{aligned}
f_x&=2x\sin y\\
f_y&=x^2\cos y.
\end{aligned}

In our case, we can use the Chain Rule and the Product Rule to find $f_{xx}$ when $f(x,\,y)=e^{x^2\,+\,y^3}$. After this, $f_{xxyy}$ can be found similarly.