Difference between revisions of "Derivative of sech"
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<strong>[[Derivative of sech|Theorem]]:</strong> The following formula holds: | <strong>[[Derivative of sech|Theorem]]:</strong> The following formula holds: | ||
| − | $$\dfrac{\mathrm{d}}{\mathrm{d} | + | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{sech}(z)=-\mathrm{sech}(z)\mathrm{tanh}(z),$$ |
where $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]] and $\mathrm{tanh}$ denotes the [[tanh|hyperbolic tangent]]. | where $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]] and $\mathrm{tanh}$ denotes the [[tanh|hyperbolic tangent]]. | ||
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Revision as of 08:28, 16 May 2016
Theorem: The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{sech}(z)=-\mathrm{sech}(z)\mathrm{tanh}(z),$$ where $\mathrm{sech}$ denotes the hyperbolic secant and $\mathrm{tanh}$ denotes the hyperbolic tangent.
Proof: █
