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Math Help - Logarithmic Differentiation

  1. #1
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    Feb 2009
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    Logarithmic Differentiation

    Use logarithmic differentiation to find the derivative of the function:
    y=3x^{cos(4x)}

    This is the steps I took:
    ln(y)=ln(3x^{cos(4x)})
    ln(y)=ln(3)+cos(4x)ln(x)
    \frac{y'}{y}=1/3+(-4sin(4x)ln(x)+cos(4x)\frac{1}{x})
    y'=3x^{cos(4x)}(\frac{1}{3}-4sin(4x)ln(x)+cos(4x)\frac{1}{x})
    y'=x^{cos(4x)}-\frac{4}{3}sin(4x)ln(x)x^{cos(4x)}+3cos4x^{cos(4x)-1)}

    What did I do wrong?
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  2. #2
    Member
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    Jan 2009
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    ln(3) is a number.
    the derivative of a number is 0.
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