Is it really true that "if a function is discontinuous, automatically, it's not differentiable"?
35671
Why can a discontinuous function not be differentiable?
103241
A function that is continuous at the origin but not differentiable there
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
87131
Discontinuous at rationals and differentiable at irrationals?
118048
Can a function with just one point in its domain be continuous?
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
67791
Can I exchange limit and differentiation for a sequence of smooth functions?
62352
Proving a scalar function is differentiable at the origin but that its partial derivatives are not continuous at that point.
83915
Showing that a function is not differentiable
22392
How can a function with a hole (removable discontinuity) equal a function with no hole?
118192
Is there a bijective function $f: \mathbb{R}\to\mathbb{R}$ that is discontinuous?
85623
Proof of continuity implied by differentiability
148737
Is $|xy|$ differentiable in $(0,0)$?
27888
Why is $|x|$ not differentiable at $x=0$?
64797
Does an absolutely integrable function tend to $0$ as its argument tends to infinity?
8321
Why differentiability implies continuity, but continuity does not imply differentiability?
4679
Nonpiecewise Function Defined at a Point but Not Continuous There