Question

How do you differentiate `f(x) =tan(x + sec x)`?

Answer 1

`sec^2(x + secx)(1 + secxtanx)`

Explanation:

Using the`color(blue) " chain rule "`

`d/dx[f(g(x)] = f'(g(x)) . g'(x)`

and the standard derivatives

`d/dx(tanx) = sec^2x " and " d/dx(secx) = secxtanx`

`rArr f'(x) = sec^2(x +secx) d/dx(x+secx)`

`= sec^2(x + secx).(1 + secxtanx )`