Is a continuous real-valued function with an almost everywhere continuous derivative necessarily differentiable on $\mathbb{R}$?
25592
If a derivative of a continuous function has a limit, must it agree with that limit?
30590
Are "most" continuous functions also differentiable?
127114
Differentiability implying continuity
98772
Continuity of a function in $\mathbb{R}$
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
135199
Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous
42900
Locally continuously differentiable implies locally Lipschitz
120947
continuous real-valued function
136011
Must $f$ be continuous?
76908
If $f'$ is differentiable at $a$ then $f'$ is continuous at $(a-\delta,a+\delta)$
73594
Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$
150833
Discontinuities of the derivative of a differentiable function on closed interval
35671
Why can a discontinuous function not be differentiable?
114691
Why can't differentiability be generalized as nicely as continuity?
120118
The distinction between infinitely differentiable function and real analytic function
66560
Is a differentiable function always continuous?
25482
If a function is continuous and differentiable everywhere is the derivative continuous?