Use the Quotient Rule to differentiate the function .

Question

Use the Quotient Rule to differentiate the function  .

Quizplus · Accepted Answer

The quotient rule states that if $f(x) = \frac{g(x)}{h(x)}$, then $f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{h(x)^2}$. Applying this to the given function, we have $g(x) = 11$ and $h(x) = e^{ax}$. Thus, $g'(x) = 0$ and $h'(x) = ae^{ax}$. Plugging these into the quotient rule formula, we get:

$f'(x) = \frac{0\cdot e^{ax} - 11\cdot ae^{ax}}{(e^{ax})^2} = -\frac{11a}{e^{ax}}$

Therefore, the correct answer is B, which is $11e^{ax}\left(-\frac{a}{e^{ax}}\right) = -11ae^{ax}$.

Use the Quotient Rule to Differentiate the Function