Derivative of Secant Function

Theorem

 * $D_x \left({\sec x}\right) = \sec x \tan x$

where $\cos x \ne 0$.

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

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

Then:

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