Difference between revisions of "Derivative of arcsec"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following formula holds: $$\dfrac{d}{dz} \mathr...") |
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<strong>[[Derivative of arcsec|Theorem]]:</strong> The following formula holds: | <strong>[[Derivative of arcsec|Theorem]]:</strong> The following formula holds: | ||
| − | $$\dfrac{d}{ | + | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{arcsec}(z) = -\dfrac{1}{\sqrt{z^2-1}|z|},$$ |
where $\mathrm{arcsec}$ is the [[arcsec|inverse secant]] function. | where $\mathrm{arcsec}$ is the [[arcsec|inverse secant]] function. | ||
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Revision as of 23:08, 15 May 2016
Theorem: The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{arcsec}(z) = -\dfrac{1}{\sqrt{z^2-1}|z|},$$ where $\mathrm{arcsec}$ is the inverse secant function.
Proof: █
