How do you differentiate y=e^((2x)/3)?

1 Answer
Jul 21, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2}{3} {e}^{\frac{2 x}{3}}$

Explanation:

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

$\frac{d}{\mathrm{dx}} \left({e}^{x}\right) = {e}^{x}$

and using the $\textcolor{b l u e}{\text{chain rule}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left({e}^{g \left(x\right)}\right) = {e}^{g \left(x\right)} g ' \left(x\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{\frac{2 x}{3}} . \frac{d}{\mathrm{dx}} \left(\frac{2}{3} x\right) = \frac{2}{3} {e}^{\frac{2 x}{3}}$