Derivative of Hyperbolic Cotangent of a x

Theorem

$\map {\dfrac \d {\d x} } {\coth a x} = -a \csch^2 a x$

Proof

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

\(=\)

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

Derivative of $\coth x$

\(\ds \leadsto \ \ \)

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

\(=\)

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

Derivative of Function of Constant Multiple

$\blacksquare$

Also see

• Derivative of $\tanh a x$