Difference between revisions of "Derivative of hyperbolic cosecant"
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| − | <strong>[[Derivative of hyperbolic cosecant| | + | <strong>[[Derivative of hyperbolic cosecant|Theorem]]:</strong> The following formula holds: |
$$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{csch}(z)=-\mathrm{csch}(z)\mathrm{coth}(z),$$ | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{csch}(z)=-\mathrm{csch}(z)\mathrm{coth}(z),$$ | ||
where $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]] and $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]]. | where $\mathrm{csch}$ denotes the [[csch|hyperbolic cosecant]] and $\mathrm{coth}$ denotes the [[coth|hyperbolic cotangent]]. | ||
Revision as of 08:21, 16 May 2016
Theorem: The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{csch}(z)=-\mathrm{csch}(z)\mathrm{coth}(z),$$ where $\mathrm{csch}$ denotes the hyperbolic cosecant and $\mathrm{coth}$ denotes the hyperbolic cotangent.
Proof: █
