# Derivative of Hyperbolic Sine/Proof 3

$\map {\dfrac \d {\d x} } {\sinh x} = \cosh x$
 $\ds \map {\frac \d {\d x} } {\sinh x}$ $=$ $\ds -i \map {\frac \d {\d x} } {\sin i x}$ 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
$\blacksquare$