Question

let $f(x)=\frac{1}{e^{x}}$. find $f(x)$. choose 1 answer:

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 1$ and $v=e^{x}-x$.

Step2: Find $u'$ and $v'$

Since $u = 1$, then $u'=0$. Since $v = e^{x}-x$, then $v'=e^{x}-1$.

Step3: Apply quotient - rule

$f'(x)=\frac{u'v - uv'}{v^{2}}=\frac{0\times(e^{x}-x)-1\times(e^{x}-1)}{(e^{x}-x)^{2}}=\frac{1 - e^{x}}{(e^{x}-x)^{2}}$.

Answer:

$\frac{1 - e^{x}}{(e^{x}-x)^{2}}$