# sinh

• June 18th 2008, 09:54 PM
kate45
sinh
hi there,

can anyone help me with the derivative of sinh(3x)
• June 18th 2008, 09:59 PM
TheEmptySet
Quote:

Originally Posted by kate45
hi there,

can anyone help me with the derivative of sinh(3x)

$\sinh(3x)=\frac{e^{3x}-e^{-3x}}{2}$

$\cosh(3x)=\frac{e^{3x}+e^{-3x}}{2}$

$\frac{d}{dx}\sinh(3x)=\frac{d}{dx}\left( \frac{e^{3x}-e^{-3x}}{2}\right)=3\left( \frac{e^{3x}+e^{-3x}}{2}\right)=3\cosh(3x)$
• June 19th 2008, 07:15 AM
kalagota
or simply, if you already know the derivative of sinh x, just apply chain rule..