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Possible Duplicate:
Why should I go on and differentiate this?

Some help please, I know how to differentiate $\cos x$ but what about $\frac{d}{dx}\cos\left(\frac{y}{x^4}\right)?$ I tried to plug it into the definition but with no success.

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    I answered this in your question http://math.stackexchange.com/questions/82061/why-should-i-go-on-and-differentiate-this/82063#82063 three hours ago. Please do not duplicate.2011-11-14

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NOTE: I see now that this is the more or less same answer as given by Ross here, and that the OP asked the question twice.

I will explain how to do it without using the definition of a derivative.

We are to differentiate $\cos \left( \dfrac{y}{x^4} \right)$. Then the derivative of $\cos$ is $-\sin$, so we get $-\sin \left( \dfrac{y}{x^4} \right) \cdot \left( \dfrac{y}{x^4} \right)'$. What is $\left( \dfrac{y}{x^4} \right)'$?

$\left( \dfrac{y}{x^4} \right)' = y \cdot \dfrac{-4}{x^5} + y' \cdot \dfrac{1}{x^4}$

Of course, knowing nothing more about $y$, we cannot simplify $y'$.