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