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Math Help - How do you find the derivative of this function?

  1. #1
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    How do you find the derivative of this function?

    f(x)=(x^4+1)^(sinx)

    Can somebody show me the steps?
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  2. #2
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    Re: How do you find the derivative of this function?

    Quote Originally Posted by littleblackdress View Post
    f(x)=(x^4+1)^(sinx)

    Can somebody show me the steps?
    Logarithmic Differentiation
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  3. #3
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    Re: How do you find the derivative of this function?

    Quote Originally Posted by littleblackdress View Post
    f(x)=(x^4+1)^(sinx)

    Can somebody show me the steps?
    y=(x^4+1)^(sinx)

    ln(y)
    =ln((x^4+1)^(sinx)
    =(sinx)ln(x^4+1)
    d/dx(lny)=d/dx((sinx)ln(x^4+1))
    (1/y)y'=(sinx)((4x^3)/(x^4+1))+((cosx)ln(x^4+1))

    now solve for y' (You already know your y which is y=(x^4+1)^(sinx) )

    f '(x)=y '
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