Use the Quotient Rule to differentiate the function .

Question

Use the Quotient Rule to differentiate the function  . ​

Quizplus · Accepted Answer

We use the quotient rule, which states that if $f$ and $g$ are functions,

$$(f/g)' = (f'g - fg')/g^2.$$

In this case,

$$f(x) = 11e^{2x} \quad 	ext{and} \quad g(x) = e^{x}.$$

Then,

$$f'(x) = 22e^{2x} \quad 	ext{and} \quad g'(x) = e^{x}.$$

Using the quotient rule, we have

\begin{align*}
\frac{d}{dx}\left(\frac{11e^{2x}}{e^x}ight) &= \frac{(22e^{2x} \cdot e^x) - (11e^{2x} \cdot e^x)}{(e^x)^2} \
&= \frac{11e^{3x}}{e^{2x}} \
&= 11e^x.
\end{align*}

Therefore, the answer is (B).

Use the Quotient Rule to Differentiate the Function