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Math Help - Derivative of exponential function

  1. #1
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    Derivative of exponential function

    (x+cot (x))^sin (x^2)

    I tried solving the problem by taking a log with base (x+cot (x))
    Is it acceptable to take a log with a variable base ??
    If not, please I would have the solution of the problem.

    Thanks in advance !!
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  2. #2
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    Quote Originally Posted by egt2010 View Post
    (x+cot (x))^sin (x^2)

    I tried solving the problem by taking a log with base (x+cot (x))
    Is it acceptable to take a log with a variable base ??
    If not, please I would have the solution of the problem.

    Thanks in advance !!

    Since a^b=e^{b\ln a} , we get (x+\cot x)^{\sin x^2}=e^{\sin x^2\ln (x+\cot x)}. Apply now the chain rule.

    Tonio
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