# Derivative of Hyperbolic Sine/Proof 3

Jump to navigation
Jump to search

## Theorem

- $\map {\dfrac \d {\d x} } {\sinh x} = \cosh x$

## Proof

\(\ds \map {\frac \d {\d x} } {\sinh x}\) | \(=\) | \(\ds -i \map {\frac \d {\d x} } {\sin i x}\) | 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 |

$\blacksquare$