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, $$\sec x = \frac {1} {\cos x}$$.
 * From Derivative of Cosine Function we have $$D_x \left({\cos x}\right) = -\sin x$$.

Then:

$$ $$ $$

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