Question

What is the derivative of `y=sec(2x) tan(2x)`?

Answer 1

2sec(2x)`(sec^2(2x) + tan^2(2x))`

Explanation:

`y' = (sec(2x))(tan(2x))' + (tan(2x))(sec(2x))'` (Product Rule)
`y' = (sec(2x))(sec^2(2x))(2) + (tan(2x))(sec(2x)tan(2x))(2)` (Chain rule and derivatives of trig)
`y' = 2sec^3(2x) + 2sec(2x)tan^2(2x)`
`y' = 2sec(2x)(sec^2(2x) + tan^2(2x))`