Question

What is the derivative of $e^{-x}$?

Answer 1

Determine the derivative of $e^{-x}$.

Let $y=e^{-x}$

Differentiate:

$$\begin{gathered} \frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\mathrm{d}}{\mathrm{d}x}.\left(-e^{-x}\right) \\ \Rightarrow \frac{\mathrm{d}}{\mathrm{d}x}{e}^{-x}=-e^{-x}(\because \frac{\mathrm{d}}{\mathrm{d}x}{e}^{nx}=n{e}^{nx}) \end{gathered}$$

Hence, the required derivative is$\frac{\mathrm{d}}{\mathrm{d}x}\left(e^{-x}\right)=-e^{-x}$.