Question

How do you differentiate `f(x)=2secx+tanx`?

Answer 1

`f'(x) =sec^2x (1 + 2sinx)`

Explanation:

Start by rewriting in terms of sine and cosine using the reciprocal/quotient identities.

`f(x) = 2/cosx + sinx/cosx`

`f(x) = (2 + sinx)/cosx`

We differentiate using the quotient rule.

`f'(x) = (cosx xx cosx - ( (2 + sinx)(-sinx)))/(cosx)^2`

`f'(x) = (cos^2x - (-2sinx - sin^2x))/(cosx)^2`

`f'(x) = (cos^2x + 2sinx + sin^2x)/cos^2x`

`f'(x) = (1 + 2sinx)/(cos^2x)`

`f'(x) =sec^2x (1 + 2sinx)`

Hopefully this helps!