Derivative of Hyperbolic Sine Function/Proof 3

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Theorem

$D_x \left({\sinh x}\right) = \cosh x$


Proof


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

$\blacksquare$