How do you find the derivative of sqrt(e^(2x) +e^(-2x))?

1 Answer
Jul 22, 2016

(dy)/(dx) = (e^(2x) - e^(-2x))/(sqrt(e^(2x) + e^(-2x))

Explanation:

y = (e^(2x) + e^(-2x))^(1/2)

We need to use the chain rule as we have y(u(x)).

In this case (dy)/(dx) = (dy)/(du)(du)/(dx)

u = e^(2x) + e^(-2x) implies (du)/(dx) = 2e^(2x) - 2e^(-2x)

(dy)/(du) = 1/2(e^(2x) + e^(-2x))^(-1/2) using the power rule

Hence:

(dy)/(dx) = 1/2(e^(2x) + e^(-2x))^(-1/2)*2e^(2x) - 2e^(-2x)

(dy)/(dx) = (e^(2x) - e^(-2x))/(sqrt(e^(2x) + e^(-2x))