Proving the differentiability.
105068
Proving that the function is differentiable and $f'(0)=0$
34136
$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
142490
Alternative proof for differentiability of inverse function?
123519
Fréchet differentiability from Gâteaux differentiability
43956
Differentiating $f(x)^{g(x)}$
57407
Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
43874
Differentiability implies continuity - A question about the proof
96022
Symmetry of second derivative - Sufficiency of twice-differentiability
4636
How to show that $f$ is differentiable at $x=0.$
95030
Proving the Cauchy-Schwarz inequality by induction
136714
Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$.
150447
Prove a differentiable function between banach spaces is continuous
8659
How do you show that $e^{-1/x^2}$ is differentiable at $0$?
137527
if $f(x)$ is differentiable at a x, prove that: $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$
30533
Showing that this function is infinitely differentiable
138864
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f(x+y)=f(x)f(y)$ and $f'(0)$ exists, then $f$ is differentiable on $\mathbb R$