Find second order mixed partial derivative, $\displaystyle \frac{\partial^{2} f}{\partial y \partial x}$ of $\displaystyle \frac{x \log(y)}{ye^x}$

I tried differentiating it wrt $x$ (keeping $y$ constant) and then differentiating the result wrt $y$ (keeping $x$ as constant) but my answer is not matching.

  • $\begingroup$ It is not a partial derivative. $\endgroup$ – Kenny Lau Jun 27 '16 at 13:15
  • $\begingroup$ Also, what is $f$? $\endgroup$ – Kenny Lau Jun 27 '16 at 13:15
  • $\begingroup$ $\dfrac{\mathrm d^2f}{\mathrm dy\ \mathrm dx}$ is really just $\dfrac{\mathrm d}{\mathrm dy}\dfrac{\mathrm df}{\mathrm dx}$. $\endgroup$ – Kenny Lau Jun 27 '16 at 13:16
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    $\begingroup$ What is your answer, and what is the book's answer? $\endgroup$ – Kenny Lau Jun 27 '16 at 13:16
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    $\begingroup$ Right...go ahead and show us what you did (and what the book said), and we can probably find the mistake pretty quickly. (About 20% of the time, the mistake is "the answer book is wrong and you're right." ) $\endgroup$ – John Hughes Jun 27 '16 at 13:20

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