Difference between revisions of "Derivative of sech"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Proposition:</strong> $\dfrac{d}{dx}$$\mathrm{sech}$$(x)=-\mat...") |
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| − | <strong>[[Derivative of sech| | + | <strong>[[Derivative of sech|Theorem]]:</strong> The following formula holds: |
| + | $$\dfrac{\mathrm{d}}{\mathrm{d}x}=-\mathrm{sech}(z)\mathrm{tanh}(z),$$ | ||
| + | where $\mathrm{sech}$ denotes the [[sech|hyperbolic secant]] and $\mathrm{tanh}$ denotes the [[tanh|hyperbolic tangent]]. | ||
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
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Revision as of 08:28, 16 May 2016
Theorem: The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}x}=-\mathrm{sech}(z)\mathrm{tanh}(z),$$ where $\mathrm{sech}$ denotes the hyperbolic secant and $\mathrm{tanh}$ denotes the hyperbolic tangent.
Proof: █
