Derivative of Cotangent Function/Corollary 1

Corollary to Derivative of Cotangent Function

$\map {\dfrac \d {\d x} } {\cot a x} = -a \csc^2 a x$

Proof

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

\(=\)

\(\ds -\csc^2 x\)

Derivative of $\cot x$

\(\ds \leadsto \ \ \)

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

\(=\)

\(\ds -a \csc^2 a x\)

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