Question

Find the second derivative of f(x)=sec(x)

Answer 1

f(x) = sec(x)
f(x) = 1
cos(x)


`(f(x + \delta x) - f(x))/(\delta x) = ((1 + \delta x) - 1)/(\delta x)`

`(f(x + \delta x) - f(x))/(\delta x) = (1 - 1 + \delta x)/(\delta x)`

`(f(x + \delta x) - f(x))/(\delta x) = (\delta x)/(\delta x)`

`(f(x + \delta x) - f(x))/(\delta x) = 1`


`(f(x + \delta x) - f(x))/(\delta x) = -sin(x)`


`sec(x)' = (1)/(-sin(x))`

`sec(x)' = -csc(x)`