Question

Which of the following is the derivative of f(x)=sec(x)(2x-tan(x)): (answers attached)

Answer 1

Following the steps,
\[f'(x)=\frac{\sin x}{\cos x}(2x-\tan x)+\frac{1}{\cos^2x}\left(2-\frac{1}{\cos^2x}\right)=\\
=\frac{2x\sin x\cos x-\sin^2x}{\cos^3x}+\frac{1}{\cos x }\left(2-1-\tan^2x\right)=\]

Answer 2

\[f'(x)=\frac{2x\sin x\cos x+3\cos^2x-2}{\cos^3x}\]So it is (c).

Answer 3

That's great! Very well presented answer, thank you so much!