\Delta y = f(x + \Delta x)-f(x)

r = \frac{\Delta y}{\Delta x}-{f}^{'}(x)

r + {f}^{'}(x) = \frac{\Delta y}{\Delta x}

{\Delta x}(r + {f}^{'}(x)) = \Delta y

r\Delta x + {f}^{'}(x)\Delta x = f(x + \Delta x)-f(x)