Difference between revisions of "Derivative of sech"
From specialfunctionswiki
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{sech}(z)=-\mathrm{sech}(z)\mathrm{tanh}(z),$$ | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{sech}(z)=-\mathrm{sech}(z)\mathrm{tanh}(z),$$ | ||
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]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
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| + | [[Category:Theorem]] | ||
Revision as of 07:05, 9 June 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.
