calculate rate of convergence of sin(x)/x

I really have no idea if this is at all relevant - I suppose I should google it.     LOL

I saw the word rate so I differentiated .    

$$\frac{d}{dx}(sinx)*x^{-1}\\\\
=(sinx)*-1x^{-2}\;+\;(cosx)*x^{-1}\\\\
=\frac{-sin(x)}{x^2}\;+\;\frac{cos(x)}{x}\\\\
=\frac{xcos(x)-sin(x)}{x^2}$$