# Math Help - Hyperbolic derivative proof

1. ## Hyperbolic derivative proof

When proving that d/dx (sinhx) = coshx, is this correct:

sinhx = (e^x-e^-x) / 2
d/dx sinhx = (e^x+e^-x)/2

Since /2 is just a constant I can leave it like that, correct? Is there any steps that I migth be missing?

2. Hello,

As 2 is a constant, yes you can.

In general, the derivative of ay, where a is a constant will be a*y'

3. ## Ok here we go

$sinh(x)=\frac{e^{x}-e^{-x}}{2}$...therefore... $\frac{D[sinh(x)]}{dx}=\frac{1}{2}[e^{x}+e^{-x}]=cosh(x)$