A function that is differentiable on irrationals but discontinuous on rationals
87131
Discontinuous at rationals and differentiable at irrationals?
101281
Does there exist a smooth function which is nowhere analytic?
18825
Integrable but not differentiable function
130019
Function that is continuous only on the transcendental numbers
118400
Is there a monotonic function discontinuous over some dense set?
30533
Showing that this function is infinitely differentiable
151575
Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable
30590
Are "most" continuous functions also differentiable?
98666
Continuity defined for rational and irrational numbers
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
83915
Showing that a function is not differentiable
130748
Infinitely differentiable function with given zero set?
62581
What is an example that a function is differentiable but derivative is not Riemann integrable
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
88240
Two functions discontinuous, but sum continuous
17440
Differentiation using first principles with rational powers
71487
Real Analysis: Continuity of a Composition Function