- #1

- 252

- 8

## Main Question or Discussion Point

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)##?

\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)##?