Question

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

y = x/e^2x

Answer 1

`y' = (1 - 2x)/(e^(4x))`

Explanation:

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

`y = (f(x))/(g(x))`

This function has the following derivative

`y' = (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' = (f'(x)*g(x) - g'(x)*f(x))/((g(x))^(2))`

`y' = (e^(2x) - 2xe^(2x))/((e^(2x))^(2))`

`y' = (e^(2x)(1 - 2x))/(e^(4x))`

`y' = (1 - 2x)/(e^(4x))`