Question

The derivative of $\left[\begin{array}{c}\frac{e^x+1}{e^x}\end{array}\right]$ is equal to

• A. 0
• B. $\frac{1}{e^x}$
• C. $-\frac{1}{e^x}$
• D. $e^x$

Answer 1

The correct option is C $-\frac{1}{e^x}$

$\frac{d}{dx}\left[\frac{e^x+1}{e^x}\right]=\frac{d}{dx}[1+\frac{1}{e^x}]=\frac{d}{dx}[1+e^{-x}]$

$\Rightarrow 0+e^{-x}(-1)$

$\therefore \frac{d}{dx}\left[\frac{e^x+1}{e^x}\right]=-e^{-x}=\frac{-1}{e^x}$