Answer to Question #139637 in Calculus for Timmy

Question

If y = sin(ex), then y’ is

Select one:
A. excos(ex)
B. xcosx
C. cos(ex)
D. xcosx-1

Answer 1

Given ,

$y=sin(e^x)$

Differentiate y With respect to x using chain rule

$\to y'=cos(e^x)\times\dfrac{d(e^x)}{dx}$

$\to y'=cos(e^x)\times e^x$

$\to y'=e^xcos(e^x)$

So option (A) is correct.