Question

How do you find the derivative of `f(x)= 5 sec(x) tan(x)` ?

Answer 1

By Product Rule, we can find
`f'(x)=5secx(1+2tan^2x)`.

Let us look at some details.
By pulling 5 out of the derivative,
`f'(x)=5[secxtanx]'`
by Product Rule,
`=5[secxtanx cdot tanx+secx cdot sec^2x]`
by factoring out `sec x`,
`=5secx(tan^2x+sec^2x)`
by `sec^2x=1+tan^2x`,
`=5secx(1+2tan^2x)`