# Derivative of Hyperbolic Sine Function/Proof 3

## 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 | $\quad$ |

$\blacksquare$