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Math Help - Partial derivative

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    Partial derivative

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    Quote Originally Posted by mr_motivator View Post
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    In this case, y can be treated as a constant.

    \frac{\partial}{\partial x}\left(\frac{1}{7} \frac{\sin(6xy)}{x^4y}\right)

    Using product rule, we can set u= \sin(6xy)\rightarrow u' = 6y\cos(6xy) and v=\frac{1}{7yx^4}\rightarrow v'=\frac{-4}{7y}\left(\frac{1}{x^5}\right).

    Product rule: \frac{\mathrm{d}(uv)}{\mathrm{d}x} = u'v+uv'

    \therefore \frac{\partial}{\partial x}\left(\frac{1}{7} \frac{\sin(6xy)}{x^4y}\right) = \left(6y\cos(6xy)\right)\left(\frac{1}{7yx^4}\righ  t) +\left(\sin(6xy)\right)\left(\frac{-4}{7y}\left(\frac{1}{x^5}\right)\right) = \frac{6xy\cos(6xy) - 4\sin(6xy)}{7yx^5}
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