What is the derivative of tan(x)?

The correct answer to this question is sec 2 x. To be able to find the derivative of tan x, one must know the derivatives of sin x is cos x. Once one knows this, they will also know that cos x is - sin x.

Once those two things are known, the following steps and formula. d x tan x = d d x sin x cos x = cos x. cos x − sin x. ( −sin x) cos 2 x which is using the Quotient Rule.= cos 2 x + sin 2 x cos 2 x = 1 cos 2 x which is using the Pythagorean Identity) = sec 2 x