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differentiate f(x)=Tan^3(e^2x +1)

  • calculus -

    Let v(x) = e^2x + 1
    dv/dx= 2 e^2x
    Let u(v) = tan^3 v

    f(x) = u[(v(x)]
    df/dx = du/dv * dv/dx

    For du/dv, let f(g) = g^3 and
    g(v) = tan v

    u = f{g(v)}
    du/dv = df/dg * dg/dv = 3 g^2 * sec^2(v)
    = 3 tan^2v*sec^2(v)

    df/dx= 2e^(2x)*3tan^2v*sec^2(v)

    Substitute e^2x +1 for v for the derivative imn terms of x.

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