Derivative of Hyperbolic Sine Function/Proof 3

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Theorem

$\map {D_x} {\sinh x} = \cosh x$


Proof


\(\displaystyle \map {D_x} {\sinh x}\) \(=\) \(\displaystyle -i \, \map {D_x} {\sin i x}\) Hyperbolic Sine in terms of Sine
\(\displaystyle \) \(=\) \(\displaystyle \cos i x\) Derivative of Sine Function
\(\displaystyle \) \(=\) \(\displaystyle \cosh x\) Hyperbolic Cosine in terms of Cosine

$\blacksquare$