# What is the derivative of f(x)=ln (x^2+2)?

May 12, 2016

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{2 x}{{x}^{2} + 2}$
Derivative of $f \left(x\right) = \ln \left({x}^{2} + 2\right)$ can be found using chain formula,
as $f \left(x\right) = \ln \left(g \left(x\right)\right)$ and $g \left(x\right) = \left({x}^{2} + 2\right)$
Hence, $\frac{\mathrm{df}}{\mathrm{dx}} = \frac{1}{{x}^{2} + 2} \times 2 x = \frac{2 x}{{x}^{2} + 2}$