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

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Answer 1 · 2016-07-22T19:37:07

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

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

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:

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

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

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