# How do you differentiate f(x) = (2x-1)(3x-2)(5x+1) ?

##### 1 Answer
May 7, 2017

There is one more method i.e. to take natural logarithms on both side and then differentiate with respect to X this will definitely simplify the calculation to much extent
$\ln f \left(x\right) = \ln \left(2 x - 1\right) + \ln \left(3 x - 2\right) + \ln \left(5 x + 1\right)$
$\implies \frac{f ' \left(x\right)}{f \left(x\right)} = \frac{2}{2 x - 1} + \frac{3}{3 x - 2} + \frac{5}{5 x + 1}$
$\therefore f ' \left(x\right) = \left(2 x - 1\right) \left(3 x - 2\right) \left(5 x + 1\right) \left[\frac{2}{2 x - 1} + \frac{3}{3 x - 2} + \frac{5}{5 x + 1}\right]$