Derivative of Hyperbolic Sine/Proof 3
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The validity of the material on this page is questionable.
The link to Derivative of Sine Function demonstrates the result in the real domain only.
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Theorem
- $\map {\dfrac \d {\d x} } {\sinh x} = \cosh x$
Proof
The link to Derivative of Sine Function demonstrates the result in the real domain only.
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| \(\ds \map {\frac \d {\d x} } {\sinh x}\) | \(=\) | \(\ds -i \map {\frac \d {\d x} } {\sin i x}\) | Hyperbolic Sine in terms of Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \cos i x\) | Derivative of Sine Function | |||||||||||
| \(\ds \) | \(=\) | \(\ds \cosh x\) | Hyperbolic Cosine in terms of Cosine |
$\blacksquare$