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Use logarithmic differentiation to find the derivative of the function. y = x9 sin(x)?

Use logarithmic differentiation to find the derivative of the function.

y = x9 sin(x)

Update:

y=x^(9sin(x))

2 Answers

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  • Pope
    Lv 7
    1 month ago

    Do you mean this?

    y = x⁹sin(x)

    ln|y| = ln|x⁹sin(x)|

    ln|y| = 9ln|x| + ln|sin(x)|

    (1/y)y' = 9/x + cot(x)

    y' = y[9/x + cot(x)]

    y' = x⁹sin(x)[9/x + cot(x)]

    y' = 9x⁸sin(x) + x⁹cos(x)

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  • ted s
    Lv 7
    1 month ago

    don't know why you would use it but .......y ' / y = 9 / x + cos x / sin x====>

    y ' = 9 x^8 sin x + x^9 cos x

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