Is f(x) differentiable at (0,0)?
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
144013
If $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.
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 $(0,0)$?
24900
Homogeneity and Differentiability at $0$ implies linearity?
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
34187
The limit of the derivative of an increasing and bounded function is always $0$?
138544
For which values of $x$, will $f (x) . f '(x) < 0$?
75932
Differentiability of $g:=f(\sqrt{x^2+y^2})$ for a $C^1$ function with $f'(0)=0$ NBHM $2008$
77624
Characterization of sets of differentiability
94193
determine whether $f(x, y) = \frac{xy^3}{x^2 + y^4}$ is differentiable at $(0, 0)$.
148737
Is $|xy|$ differentiable in $(0,0)$?
55268
Differentiable and Continuous functions on [0,1] with 'weird' conditions.
40429
Differentiability of this picewise function
21954
A question about $f(x)\equiv 0$
34136
$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
66560
Is a differentiable function always continuous?
10564
$f$ be a smooth function on real line , $f(0)=0$ , $f(x)>0, \forall x \ne 0$ and any $f^{(n)}(0)=0$ ; is $\sqrt f$ smooth?