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Math Help - ln differentiation question

  1. #1
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    ln differentiation question

    Hello, I am stuck trying to solve this problem.
    Can someone please show me the steps so I can understand the procedure.

    loge((x+2)^2(x-1)^3)


    Thanks kindly for any help.
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  2. #2
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    Re: ln differentiation question

    Quote Originally Posted by fran1942 View Post
    Hello, I am stuck trying to solve this problem.
    Can someone please show me the steps so I can understand the procedure.

    loge((x+2)^2(x-1)^3)


    Thanks kindly for any help.
    Simplify using logarithm rules first

    \displaystyle \begin{align*} \ln{ \left[ \left( x + 2 \right) ^2 \left( x - 1 \right) ^3 \right] } &= \ln{ \left( x + 2 \right) ^2 } + \ln{ \left( x - 1 \right) ^3} \\ &= 2\ln{ \left( x + 2 \right)} + 3\ln{ \left( x - 1 \right) } \end{align*}

    I'd say this looks much easier to differentiate...
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