What is the derivative of e^(-kx)?

Jul 9, 2016

$- k {e}^{- k x}$

Explanation:

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

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

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left({e}^{x}\right) = {e}^{x}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

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

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