Establish that for all real for which the derivative exists

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Establish that ddx(tan⁡x)=sec⁡2x\dfrac{d}{dx}(\tan x)=\sec^2 x for all real xx for which the derivative exists. Begin with tan⁡x\tan x expressed in terms of sin⁡x\sin x and cos⁡x\cos x and present all algebraic manipulations and limit evaluations required to justify the result.

Related theory

Browse the problem library