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  1. #1
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    logarithmic differentiation to

    Use logarithmic differentiation to find the derivative of the function


    I am getting this as an anwers:


    I know this is not the right answer.

    can u help me ?

    Thanks
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  2. #2
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    Quote Originally Posted by kashifzaidi View Post
    Use logarithmic differentiation to find the derivative of the function


    I am getting this as an anwers:


    I know this is not the right answer.

    can u help me ?

    Thanks
    note

    \ln (xy) = \ln x + \ln y

    Ok

    y=\sqrt{x} e^{x^2}(x^2+2)^5

    \ln y = \ln \left(\sqrt{x} e^{x^2} (x^2+2)^5\right)

    \ln y = \ln \sqrt{x} + \ln e^{x^2} + \ln (x^2+2)^5

    \ln y = \frac{\ln x}{2} + x^2 + 5\ln (x^2+2)

    now derive

    \frac{y'}{y} = \frac{1}{2x} + 2x + \frac{5(2x)}{x^2+2}

    y' = \left(\sqrt{x} e^{x^2}(x^2+2)^5\right)\left( \frac{1}{2x} + 2x + \frac{5(2x)}{x^2+2}\right)
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