# What is the derivative of f(x)=ln(e^x+3) ?

Aug 24, 2014

$f ' \left(x\right) = {e}^{x} / \left({e}^{x} + 3\right)$

solution

Let's $y = \ln \left(f \left(x\right)\right)$

Differentiating with respect to $x$ using Chain Rule, we get,

$y ' = \frac{1}{f} \left(x\right) \cdot f ' \left(x\right)$

Similarly following for the given problem yields,

$f ' \left(x\right) = \frac{1}{{e}^{x} + 3} \cdot {e}^{x}$

$f ' \left(x\right) = {e}^{x} / \left({e}^{x} + 3\right)$