How do I differentiate $5^{x \cos x}$? From my book, it should be implicit differentiation, but how do I start?
If I let $u = x \cos x$, then I get
$ \begin{eqnarray} \frac{dY}{dX} &=& u \cdot 5^{u - 1} \cdot \frac{du}{dX} \\ &=& x \cdot \cos x \cdot 5^{x \cos x-1} \cdot (\cos x-x \sin x) \end{eqnarray} $
I don't suppose I did it right... The correct answer is
$ \ln5 \cdot 5^{x \cos x}\cdot (\cos x-x \sin x) .$