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 $(0,0)$?
40429
Differentiability of this picewise function
100765
If $f'(x) = 0$ for all $x \in \mathbb{Q}$, is $f$ constant?
59063
$f(f(x))=f(x)$ question
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
9270
Differentiable function, with $f'(x)=[f(x)]^2$
144323
Differentiation of a function
109896
Proving that the function $f(x,y)=\frac{x^2y}{x^2 + y^2}$ with $f(0,0)=0$ is continuous at $(0,0)$.
16375
Is the function differentiable at $0$?
134880
Is there a difference between $y(x)$ and $f(x)$
77133
$g'(x) = \frac{1}{x}$ for all $x > 0$ and $g(1) = 0$. Prove that $g(xy) = g(x) + g(y)$ for all $x, y > 0$.
148737
Is $|xy|$ differentiable in $(0,0)$?
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
115635
Differentiability of antiderivative and continuity of derivative
18734
Showing that a function is differentiable
119042
If $f+g$ and $f$ are differentiable at $a$, must $g$ be differentiable at $a$?
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$