Question

f(x)=sin(e^(4x))
f'(x)=??

Answer 1

From the basic formula:
f(x) = sin (u), where u = g(x)
f'(x) = u'. cos(u)
We now set that:
u = e^4x
u' = 4e^4x

So, we have:
f(x) = sin(e^4x)
f'(x) = 4e^4x. cos(e^4x)