If $y=f(x)$ is differentiable at $x=a$ and $x$ changes from $a$ to $a+\Delta x$, the change $\Delta y$ in $f$ is given by $ \Delta y=f^{\prime}(a) \Delta x+\epsilon \Delta x $ in which $\epsilon \rightarrow 0$ as $\Delta x\rightarrow 0$ based on [[Differential Approximation]]