Differentiable Function

A function  $f:U\to \mathbb{R}$ defined on an open set $U\subset \mathbb{R}$ is said to be differentiable at $a\in U$ if the derivative

$f^{\prime }(a)={\lim }_{h\to 0}\frac{f(a+h)-f(a)}{h}$ exists. This implies that the function is continuous at $a$.

Related

• Differentiability Implies Continuity
• Continuous Function