Question

Find the derivative of

f(x) = sin^2 (e^sin^2 x)


I wonder if I'm right

F'(x) = 2cos(e^sin^2 x)
(sin^2 x e^sin^2 x -1)

Answer 1

not quite

if f = sin^2(u)
f' = 2sin(u) cos(u) u'
since u = e^v
u' = e^v v'

f = sin^2(e^sin^2 x)
f' = 2 sin(e^sin^2 x)cos(e^sin^2 x) * e^(sin^2 x) * 2 sinx cos x
= sin2x sin(2e^sin^2 x) e^(sin^2 x)

Answer 2

thank you very much