Derivative of Tangent Function/Corollary 1

Corollary to Derivative of Tangent Function

$\map {\dfrac \d {\d x} } {\tan a x} = a \sec^2 a x$

Proof

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

\(=\)

\(\ds \sec^2 x\)

Derivative of $\tan x$

\(\ds \leadsto \ \ \)

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

\(=\)

\(\ds a \sec^2 a x\)

Derivative of Function of Constant Multiple

$\blacksquare$

Also see

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

• Derivative of $\cot a x$

• Derivative of $\sec a x$
• Derivative of $\csc a x$