Derivative of Hyperbolic Sine of a x

Theorem

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

Proof

\(\ds \map {D_x} {\sinh x}\)

\(=\)

\(\ds \cosh x\)

Derivative of $\sinh x$

\(\ds \leadsto \ \ \)

\(\ds \map {D_x} {\sinh a x}\)

\(=\)

\(\ds a \cosh a x\)

Derivative of Function of Constant Multiple

$\blacksquare$

Also see

• Derivative of $\cosh a x$