Derivative of Hyperbolic Sine/Proof 3
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Theorem
- $\map {\dfrac \d {\d x} } {\sinh x} = \cosh x$
Proof
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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 |
$\blacksquare$