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I How to Convert this Derivative?

  1. Jun 17, 2016 #1
    I have a derivative of a function with respect to ##\log \left(r\right)##:

    \begin{equation*}
    \frac{dN\left(r\right)}{d \log\left(r\right)} = \frac{N}{\sqrt{2\pi} \log\left(\sigma\right)} \exp\left\{-\frac{\left[\log \left(r\right) - \log\left(r_M\right)\right]^2}{2 \left[\log\left(\sigma\right)\right]^2}\right\}
    \end{equation*}

    I need to know the derivative of this function with respect to ##r##, that is ##\frac{dN\left(r\right)}{dr}##, how shall I do this? I was told that I just need to multiply the function with the derivative of the logarithm, that is

    \begin{equation*}
    \frac{dN\left(r\right)}{dr} = \frac{dN\left(r\right)}{d \log\left(r\right)} \cdot \frac{d \log\left(r\right)}{dr}
    \end{equation*}

    Is this correct? Even though ##N\left(r\right)## is a function of ##\log\left(r\right)##?
     
  2. jcsd
  3. Jun 17, 2016 #2

    Delta²

    User Avatar
    Gold Member

    Yes this is correct, it is a well known theorem for the derivative of the composition of two functions (in your case the two functions are N(y) and y(r)=logr)), known as chain rule for derivatives.

    https://en.wikipedia.org/wiki/Chain_rule
     
  4. Jun 19, 2016 #3

    Ssnow

    User Avatar
    Gold Member

    Yes, its correct, it is the chain rule in one variable.
     
  5. Jun 30, 2016 #4
    Alright. Thank you for your help!
     
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