Derivative of Hyperbolic Sine/Proof 3

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

$\blacksquare$

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