Difference between revisions of "Derivative of coth"
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| − | <strong>[[Derivative of coth| | + | <strong>[[Derivative of coth|Theorem]]:</strong> The following formula holds: |
$$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{coth}(z) = -\mathrm{csch}^2(z),$$ | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{coth}(z) = -\mathrm{csch}^2(z),$$ | ||
where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]] and $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]]. | where $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]] and $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]]. | ||
Revision as of 08:24, 16 May 2016
Theorem: The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{coth}(z) = -\mathrm{csch}^2(z),$$ where $\mathrm{coth}$ denotes the hyperbolic cotangent and $\mathrm{csch}$ denotes the hyperbolic cosecant.
Proof: █
