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Let $f(x,y,z) = e^{xy^2}$. Find $f_{xxy}$.

How do I start approaching this question. Thanks in advance.

meta_warrior
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    Your final answer should be $2y^3e^{xy^2} (2 + xy^2 )$ – meta_warrior Nov 15 '13 at 04:57
  • I should add that because $f$ is continuously differentiable, it is probably easier to take the two derivatives with respect to x first and get $f(x,y) = y^{4}\cdot e^{x\cdot y^{2}}$. Then it becomes a much simpler problem with no additional work. – Christopher K Nov 15 '13 at 05:19

1 Answers1

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$f_{xxy}$ is shorthand for the partial derivative

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

So begin by computing the derivative of $f$ with respect to $y$, using the chain rule; then differentiate twice with respect to $x$.