Derivative of Secant Function

Theorem

 * $D_x \left({\sec x}\right) = \sec x \tan x$, when $\cos x \ne 0$.

Proof

 * From the definition of the secant function:
 * $\sec x = \dfrac 1 {\cos x} = \left({\cos x}\right)^{-1}$


 * From Derivative of Cosine Function we have:
 * $D_x \left({\cos x}\right) = -\sin x$

Then:

This is valid only when $\cos x \ne 0$.