# How do you find the derivative of f(x)=ln (x^2+2)?

May 7, 2018

$\frac{2 x}{{x}^{2} + 2}$

#### Explanation:

Chain rule: $\frac{d}{\mathrm{dx}} f \left(g \left(x\right)\right) = f ' \left(g \left(x\right)\right) g ' \left(x\right)$

$\implies \frac{d}{\mathrm{dx}} \ln f \left(x\right) = \frac{f ' \left(x\right)}{f} \left(x\right)$

$\implies \frac{d}{\mathrm{dx}} \ln \left({x}^{2} + 2\right) = \frac{\frac{d}{\mathrm{dx}} \left({x}^{2} + 2\right)}{{x}^{2} + 2}$

$\therefore = \frac{2 x}{{x}^{2} + 2}$