Show that a convex function in $\mathbb{R}^n$ is differentiable
86643
Convex function almost surely differentiable.
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
111470
Proof of differentiability of $f(x)$
125175
convexity proof of a function including ln and sums
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
147420
Equivalent definitions of convexity for $f\in\mathcal C^1(\mathbb R^n)$
142870
Prove the function is not differentiable at (0,0)
135199
Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous
78229
Proving that the tangent to a convex function is always below the function
10352
Prove that $x^n$ is a convex function on $(0,\infty)$
107321
How to show convexity of a ball in metric space?
54600
Is a convex and lower semicontinuous function defined on a closed and convex subset of $\mathbb{R}^n$ continuous?
77624
Characterization of sets of differentiability
116382
Showing convexity of a function with the restriction over an arbitrary line
129081
Proof that convex open sets in $\mathbb{R}^n$ are homeomorphic?
91123
A convex function is differentiable at all but countably many points
143491
Show that $f$ is differentiable on $(−1, 1)$.