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If f(x)=6arcsin(x4), find f'(x).

  • Calculus -

    f' = 6/√(1-x^8) * 4x^3 = 24x^3/√(1+x^8)

    recall that f=6arcsin(x^4), so
    sin(f/6) = x^4
    1/6 cos(f/6) f' = 4x^3
    f' = 24x^3/cos(f/6)

    but cos(f/6) = √(1-sin^2(f/6)) = √(1-x^8)

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