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Calc

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Find the f'(3) of F(x)=9(sin(x))^x

  • Implicit diff. - ,

    take log on both sides, and differentiate. Solve for y'.

    y=9sin(x)^x
    ln(y)=ln(9)+x*ln(sin(x))
    differentiate:
    (1/y)y' = ln(sin(x))+(x/sin(x))*cos(x)
    y'=y(ln(sin(x))+(x/sin(x))*cos(x))
    =9sin(x)^x * (ln(sin(x))+(x/sin(x))*cos(x))

    Simplify the answer and check.

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