If [math]f\left(x\right)=u\left(x\right)v\left(x\right)[/math], the multiplication rule indicates [math]f'\left(x\right)=u'\left(x\right)v\left(x\right)+u\left(x\right)v'\left(x\right)[/math]. [br]Apply the multiplication rule to [math]u\left(x\right)[/math] and [math]\frac{1}{v\left(x\right)}[/math] to obtain the division rule [math]\frac{u'\left(x\right)v\left(x\right)-u\left(x\right)v'\left(x\right)}{\left(v\left(x\right)\right)^2}[/math]. Experiment below with various [math]u[/math] and [math]v[/math].