If $f(x)$ is differentiable over $(a,b)$, does that mean $f'(x)$ is continuous over $(a,b)$?
16291
Discontinuous derivative.
32571
Is the maximum function of a continuous function continuous?
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
8836
If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
4636
How to show that $f$ is differentiable at $x=0.$
154881
Question on differentiability of a continuous function
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
87819
What is the difference between continuous derivative and derivative?
43874
Differentiability implies continuity - A question about the proof
86327
If the absolute value of a function is continuous, is the function continuous?
103241
A function that is continuous at the origin but not differentiable there
106013
Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
78834
if f(x) if differentiable and continuous, prove $\frac{af(a)-bf(b)}{a-b} = f(c) + cf'(c) $
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$