How would I differentiate the function $\ln\dfrac{x-1}{x^3}$ by applying the properties of logarithms?

I've already differentiated using chain rule and got $-\dfrac{2x-3}{(x-1)x}$.

However, I'm not sure how to do so with the properties of logarithms.

  • 1
    $\begingroup$ Lookup "logarithmic derivative". $\endgroup$ – Yves Daoust Jun 25 '19 at 11:40

Hint:$$\ln\frac{x-1}{x^3} = \ln(x-1) - 3\ln(x)$$


You should use $\ln \frac{a}{b}=\ln a - \ln b$ and then take the derivative.


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