Question

Differentiating Exponential Functions In Exercise, find the derivative of the function.

Answer 1

Answer:

$y' = \frac{1 - 2x}{e^{4x}}$

Step-by-step explanation:

If we have a quotient function y, in the following format

$y = \frac{f(x)}{g(x)}$

This function has the following derivative

$y' = \frac{f'(x)*g(x) - g'(x)*f(x)}{(g(x))^{2}}$

In this problem, we have that:

$f(x) = x, g(x) = e^{2x}$

So

$f'(x) = 1, g'(x) = 2e^{2x}$

The derivative of the function is:

$y' = \frac{f'(x)*g(x) - g'(x)*f(x)}{(g(x))^{2}}$

$y' = \frac{e^{2x} - 2xe^{2x}}{(e^{2x})^{2}}$

$y' = \frac{e^{2x}(1 - 2x)}{e^{4x}}$

$y' = \frac{1 - 2x}{e^{4x}}$