A function $f$ is twice differentiable and $|f|\leq M_0$, $|f''|\leq M_2$, show that $|f'|\leq 2\sqrt{M_0M_2}$
134382
Proving bounded first derivative
43956
Differentiating $f(x)^{g(x)}$
2414
If $f \in \operatorname{Hol}(D)$, $f(\frac{1}{2}) + f(-\frac{1}{2}) = 0$, prove that $|f(0)| \leq \frac{1}{4}$
136403
Prove that $\sqrt{a}\leq\frac{1+a}{2}$
158647
If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
105999
An application of derivatives problem- to show that $f(x+2)-f(x)>2$ for $f(x)=x\cos(1/x)$
22294
Maximum and minimum value of $\int_0^1 f(x)dx $ given $|f'(x)|<2$
97558
Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
105068
Proving that the function is differentiable and $f'(0)=0$
145496
Show $\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$ Proof verification
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
111186
Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$
69804
Prove that if $f$ is entire and $\vert f(z^2) \vert \leq 2 \vert f(z) \vert$, then $f$ is constant
80650
Complex differentiability of $f(z)=|z|$