Question

quotient rule: problem 1 (1 point) suppose that $f(x)=\frac{x + 20}{e^{x}}$. find $f(2)$. $f(2)=square$ preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor page generated september 23, 2025 at 6:32:56 pm cdt webwork © 1996 - 2024 | theme: math4 | ww_version 2.19 | pg_version 2.19 the webwork project

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. For $f(x)=\frac{x + 20}{e^{x}}$, let $u=x + 20$ and $v = e^{x}$. Then $u'=1$ and $v'=e^{x}$.

Step2: Apply quotient - rule

$f'(x)=\frac{1\times e^{x}-(x + 20)\times e^{x}}{(e^{x})^{2}}=\frac{e^{x}-(x + 20)e^{x}}{e^{2x}}=\frac{e^{x}(1-(x + 20))}{e^{2x}}=\frac{1-(x + 20)}{e^{x}}=\frac{-x - 19}{e^{x}}$.

Step3: Evaluate $f'(2)$

Substitute $x = 2$ into $f'(x)$. $f'(2)=\frac{-2-19}{e^{2}}=\frac{-21}{e^{2}}$.

Answer:

$\frac{-21}{e^{2}}$