Differentiability of a non-continuous function
136412
Differentiable at $x=a$ implies continuous at $x=a$
135449
Prove: $\frac1x$ is not a uniformly continuous function
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
151575
Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable
16291
Discontinuous derivative.
11167
A counterexample of a differentiable function on an interval whose derivative is discontinuous
86860
Continuity of differentiable function $x^2\sin(1/x)$
150833
Discontinuities of the derivative of a differentiable function on closed interval
97382
Continuous differentiability implies Lipschitz continuity
76908
If $f'$ is differentiable at $a$ then $f'$ is continuous at $(a-\delta,a+\delta)$
145173
$f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
8321
Why differentiability implies continuity, but continuity does not imply differentiability?
75932
Differentiability of $g:=f(\sqrt{x^2+y^2})$ for a $C^1$ function with $f'(0)=0$ NBHM $2008$
157347
continuity, discontinuity derivative and relation to being derivative but its partials are not continuous
142490
Alternative proof for differentiability of inverse function?
66560
Is a differentiable function always continuous?
53376
A continuous, nowhere differentiable but invertible function?