Answer to Question #204095 in Calculus for moe

Question

Determine the derivative of $y = e$ ^cos2$^x$

Answer 1

Let us determine the derivative of $y = e^{\cos 2x}$ using chain rule $(f(g(x)))'=f'(g(x))\cdot g'(x).$

$y'=e^{\cos 2x}(\cos 2x)'=e^{\cos 2x}(-\sin 2x)(2x)'=-2\sin 2xe^{\cos 2x}.$