Continuity of the derivative at a point given certain hypotheses
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
134752
Proof (epsilon delta) for the continuity of a function at a point
58664
Proving a function is continuous for a fixed variable
26955
Continuous at exactly two points and differentiable at exactly one of them
49408
Proof of the derivative of ln(x)
86860
Continuity of differentiable function $x^2\sin(1/x)$
96022
Symmetry of second derivative - Sufficiency of twice-differentiability
13257
How to prove this problem about uniform continuity
115712
Application of Derivatives rigorous proof
152590
At most finitely many (Hamel) coordinate functionals are continuous - different proof
83676
Condition for continuity of bilinear form
49587
Does a differentiable everywhere function have a continuous derivative?
57839
Real analysis: density and continuity
115417
Continuity of $L^1$ functions with respect to translation
143564
Uniform convergence of derivatives, Tao 14.2.7.
109570
How to show that the set of points of continuity is a $G_{\delta}$
25482
If a function is continuous and differentiable everywhere is the derivative continuous?