If $y$ is continuously differentiable and $y' \leq 1-y^2$ then $|y| \leq 1$
56958
bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
34136
$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
144013
If $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.
55125
Continuous right derivative implies differentiability
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
49705
Is $f(x,y)=(x+2y+y^2+|xy|, 2x+y+x^2+|xy|)$ differentiable?
16375
Is the function differentiable at $0$?
107894
Inequality involving the sup of a function and its first and second derivatives
129324
Let $f:[0;1]\to\mathbb R$ be continiously differentiable
85623
Proof of continuity implied by differentiability
115635
Differentiability of antiderivative and continuity of derivative
149764
If $f$ s twice differentiable and satisfies the following constraints, prove $f'(0)>-\sqrt 2$
58664
Proving a function is continuous for a fixed variable
86860
Continuity of differentiable function $x^2\sin(1/x)$
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
127114
Differentiability implying continuity