A function is defined by f(x) = x² for x ≤ 1 and f(x) = ax + b for x > 1…

$f'(a) = \displaystyle\lim_{h \to 0}\frac{f(a + h) - f(a)}{h}$, and $f$ is differentiable at $a$ when the left and right derivatives are equal. A differentiable function is continuous. The chain rule is $\dfrac{dy}{dx} = \dfrac{dy}{du}\times\dfrac{du}{dx}$.