# How do you differentiate  f(x)= (x^2+1) (x+2)^2 (x-3)^3 using the product rule?

Jan 17, 2018

take log

#### Explanation:

after taking log
$\log \left(f \left(x\right)\right) = \log \left({x}^{2} + 1\right) + 2 \log \left(x + 2\right) + 3 \log \left(x - 3\right)$
now differentiating
$\frac{1}{f} \left(x\right) \cdot {f}^{'} \left(x\right) = 2 \frac{x}{{x}^{2} + 1} + \frac{2}{x + 2} + \frac{3}{x - 3}$
now take f(x) to the other side and place it value
hence ${f}^{'} \left(x\right)$ can be found
hope u find it helpful :)