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.

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- Jun 9th 2009, 12:26 AMswimmergirlHigher 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. - Jun 9th 2009, 03:30 AMScott H
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.