Question

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

Answer 1

By Product Rule, we can find
`y'=secx(1+2tan^2x)`.

Let us look at some details.
`y=secxtanx`

By Product Rule,
`y'=secxtanx cdot tanx+secx cdot sec^2x`

by factoring out `sec x`,
`=secx(tan^2x+sec^2x)`

by `sec^2x=1+tan^2x`,
`=secx(1+2tan^2x)`