Behaviour of $f'(x)$ and $f''(x)$
35264
Must a monotone function have a monotone derivative?
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
41037
Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$ under some conditions
142873
What does the function f: x ↦ y mean?
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
58943
If $f'(x)\le g'(x)$, prove $f(x)\le g(x)$
141522
$f$ is T periodic and $f(x) + f'(x) \ge 0 \Rightarrow f(x) \ge 0$
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
23465
When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?
113888
Behavior of derivative near the zero of a function.
144323
Differentiation of a function
32063
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
111470
Proof of differentiability of $f(x)$
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
150502
If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$
30204
Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$