A differentiable function with f(0) = 0 and |f'(x)| < |f(x)|. Prove that f is the 0 function.
55268
Differentiable and Continuous functions on [0,1] with 'weird' conditions.
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
113343
$f$ is constant if derivative equals zero
30860
Prove that $f(x)=0$ in $[-1,1]$.
136714
Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$.
128495
Integral Inequality $|f''(x)/f(x)|$
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
96973
If $F(0,0)=0$ and $F(x,y)= \frac{xy}{x^2+y^2}$ for $(x,y)\neq (0,0)$ then $F$ is differentiable at $(0,0)$?
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
75390
How does one prove that if function's partial derivative respect to every variable is zero, function is constant?
74583
Prove that $f'(0)=L$.
151819
A twice differentiable function $f$ satisfies $f′′(x)+f(x)=−xg(x)f′(x)$, $\forall x\ge 0$.
137527
if $f(x)$ is differentiable at a x, prove that: $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$
131357
Prove that $f(x,y)=xy$ is differentiable using the definition
78319
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
18734
Showing that a function is differentiable