Difference between revisions of "Derivative of arccoth"
From specialfunctionswiki
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The following formula holds: | The following formula holds: | ||
$$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{arccoth}(z) = \dfrac{1}{z^2-1},$$ | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{arccoth}(z) = \dfrac{1}{z^2-1},$$ | ||
| − | where $\mathrm{arccoth}$ | + | where $\mathrm{arccoth}$ denotes the [[arccoth|inverse hyperbolic cotangent]]. |
==Proof== | ==Proof== | ||
Latest revision as of 01:38, 16 September 2016
Theorem
The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{arccoth}(z) = \dfrac{1}{z^2-1},$$ where $\mathrm{arccoth}$ denotes the inverse hyperbolic cotangent.
