Question

Calculate the derivative of the following function.

g(x)=sin(x^2)+(sinx)^2+sin(2x)+(sin2)x

Answer 1

\[y=f(g(x)) =>y'=f'(g(x))g'(x)\]
use chain rule

Answer 2

could you write the process?

Answer 3

you have to take the derivative of 4 terms. we already did the last one

Answer 4

derivative of
\[\frac{d}{dx}\sin(x^2)=\cos(x^2)\times \frac{d}{dx}x^2=2x\cos(x^2)\] for the first term

Answer 5

g'(x)=2 cos(2 x)+2 x cos(x^2)+sin(2)+sin(2 x)