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Math Help - Derivatives

  1. #1
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    Derivatives

    find the derivative of:
    10x^(ln(x))
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  2. #2
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    Quote Originally Posted by Asuhuman18 View Post
    find the derivative of:
    10x^(ln(x))
    You need to apply the technique called logarithmic differentiation. have you been taught it?

    Alternatively, re-write the function as 10 e^{\ln (x^{\ln x})} = 10 e^{\ln (x) \cdot \ln (x)} = 10 e^{[\ln (x)]^2} and then apply the chain rule a couple of times.
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    how would you apply chain rule to that function?
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    Quote Originally Posted by Asuhuman18 View Post
    how would you apply chain rule to that function?
    Start by letting u = [\ln (x)]^2. Please attempt the calculations before asking for more help. Post what you did and clearly state where you get stuck.
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  5. #5
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    [ln(x)]^2
    2[ln(x)]*[1/x]=2ln(x)/x. is this right?
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    Quote Originally Posted by Asuhuman18 View Post
    [ln(x)]^2
    2[ln(x)]*[1/x]=2ln(x)/x. is this right?
    That is the correct answer for \frac{du}{dx}. Now substitute the result into the chain rule formula.
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