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Math Help - differential log problem

  1. #1
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    differential log problem

    Hi, this should be pretty easy for the helpers out there. Find the derivative of loge pi^x

    Thank you
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  2. #2
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    Quote Originally Posted by slaypullingcat View Post
    Hi, this should be pretty easy for the helpers out there. Find the derivative of loge pi^x
    By "loge" do you mean the natural logarithm \ln? In that case, use the chain rule, along with

    \frac d{dx}[\ln u]=\frac{u'}u

    and

    \frac d{dx}\left[a^x\right]=(\ln a)a^x.
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  3. #3
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    thats what I ment, sorry. Can you please expand. I'm trying to teach myself this stuff. Can you show me with my questions please.
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  4. #4
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    Here it is, hopefully the extra e in the log is a mistype.

    d/dx (log (pi^x))

    using log definition of power to move the x

    d/dx [x (log (pi) )]

    then taking derivative and answer is

    log(pi)
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  5. #5
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    Quote Originally Posted by slaypullingcat View Post
    thats what I ment, sorry. Can you please expand. I'm trying to teach myself this stuff. Can you show me with my questions please.
    We use the chain rule:

    \frac d{dx}\left[\ln\pi^x\right]=\frac1{\pi^x}\cdot\frac d{dx}\left[\pi^x\right]

    =\frac{(\ln\pi)\pi^x}{\pi^x}=\ln\pi

    An even easier method is to rewrite

    \ln\pi^x=x\ln\pi

    and use the constant multiple rule.
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