Derivative of Hyperbolic Cotangent/Corollary
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Theorem
- $\map {\dfrac \d {\d x} } {\coth x} = 1 - \coth^2 x$
where $\coth x$ denotes the hyperbolic cotangent.
Proof
| \(\ds \dfrac \d {\d x} \coth x\) | \(=\) | \(\ds -\csch^2 x\) | Derivative of Hyperbolic Cotangent | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1 - \coth^2 x\) | Difference of Squares of Hyperbolic Cotangent and Cosecant |
$\blacksquare$
Sources
- 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $5$. Differential Calculus: Appendix: Derivatives of fundamental functions: $6.$ Hyperbolic trigonometric functions