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.
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 $\displaystyle f(x,\,y)=x^2\sin y$, then
$\displaystyle \begin{aligned}
f_x&=2x\sin y\\
f_y&=x^2\cos y.
\end{aligned}$
In our case, we can use the Chain Rule and the Product Rule to find $\displaystyle f_{xx}$ when $\displaystyle f(x,\,y)=e^{x^2\,+\,y^3}$. After this, $\displaystyle f_{xxyy}$ can be found similarly.