Calculus I

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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)

  • Calculus I -

    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)

  • Calculus I -

    thank you very much

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