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Math Help - Calculus Logarithmic Differentiation

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    Question Calculus Logarithmic Differentiation

    Let y=x^(cos x). Use logarithmic differentiation to find dy/dx.
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  2. #2
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    Quote Originally Posted by SoYah View Post
    Let y=x^(cos x). Use logarithmic differentiation to find dy/dx.
     \ln(y) = \ln(x^{\cos(x)})

     \ln(y) = \cos(x)\ln(x)

     \frac{1}{y} \times \frac{dy}{dx} = \cos(x)\frac{1}{x} -\sin(x)\ln(x)

      \frac{dy}{dx} = y(\cos(x)\frac{1}{x} -\sin(x)\ln(x))

      \frac{dy}{dx} = x^{\cos(x)}(\cos(x)\frac{1}{x} -\sin(x)\ln(x))
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