# How do you find the derivative of y= root3(e^x+1) ?

Sep 15, 2014

$y ' = \frac{1}{3} {\left({e}^{x} + 1\right)}^{- \frac{2}{3}} \cdot {e}^{x}$

Explanation :

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

let's $y = {\left(f \left(x\right)\right)}^{\frac{1}{3}}$, then from Chain Rule,

$y ' = \frac{1}{3} {\left(f \left(x\right)\right)}^{- \frac{2}{3}} f ' \left(x\right)$

Similarly following for the give problem and using Chain Rule, yields

$y ' = \frac{1}{3} {\left({e}^{x} + 1\right)}^{- \frac{2}{3}} \cdot {e}^{x}$