Question

How do you differentiate `f(x)=secx` using the quotient rule?

Answer 1

`f'(x) = secxtanx`

Explanation:

`f(x) = sec x`
`= 1/cos x`
`f'(x) = ([1]' * cos x - [cos x]' * 1)/cos^2x`
`=(0 * cos x - (-sin x) * 1)/cos^2x`
`=(0 + sin x)/cos^2x`
`=sinx/cos^2x`
`=sinx/cosx * 1/cosx`
`=1/cosx * sinx/cosx`
`=secx*tanx`
`=secxtanx`

Hope that helps.