Difference between revisions of "Derivative of arcsec"
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<strong>[[Derivative of arcsec|Theorem]]:</strong> The following formula holds: | <strong>[[Derivative of arcsec|Theorem]]:</strong> The following formula holds: | ||
| − | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{arcsec}(z) = | + | $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{arcsec}(z) = \dfrac{1}{z^2\sqrt{1-\frac{1}{z^2}}},$$ |
where $\mathrm{arcsec}$ is the [[arcsec|inverse secant]] function. | where $\mathrm{arcsec}$ is the [[arcsec|inverse secant]] function. | ||
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Revision as of 23:13, 15 May 2016
Theorem: The following formula holds: $$\dfrac{\mathrm{d}}{\mathrm{d}z} \mathrm{arcsec}(z) = \dfrac{1}{z^2\sqrt{1-\frac{1}{z^2}}},$$ where $\mathrm{arcsec}$ is the inverse secant function.
Proof: █
