Derivative of Secant of a x

Corollary to Derivative of Secant Function

$\map {\dfrac \d {\d x} } {\sec a x} = a \sec a x \tan a x$

Proof

\(\ds \map {\dfrac \d {\d x} } {\sec x}\)

\(=\)

\(\ds \sec x \tan x\)

Derivative of $\sec x$

\(\ds \leadsto \ \ \)

\(\ds \map {\dfrac \d {\d x} } {\sec a x}\)

\(=\)

\(\ds a \sec a x \tan a x\)

Derivative of Function of Constant Multiple

$\blacksquare$

Also see

• Derivative of $\sin a x$
• Derivative of $\cos a x$

• Derivative of $\tan a x$
• Derivative of $\cot a x$

• Derivative of $\csc a x$