$f(x,y) := \begin{cases} \frac{xy}{x^2+y^2}, &\mbox{if } (x,y) \neq (0,0)\\ 0, & \mbox{if } (x,y)=(0,0) \end{cases}$ not differentiable in $(0,0)^T$
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 $(0,0)$?
62581
What is an example that a function is differentiable but derivative is not Riemann integrable
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
31051
Is $f(x,y)=(xy)^{2/3}$ differentiable at $(0,0)$?
146888
Derivative of function with 2 variables
33499
For which $a\in \mathbb{R}$ is $f(x,y) = \frac{xy^a}{x^2+y^2}$ with $f(0,0)=0$ continuous?
34136
$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
87131
Discontinuous at rationals and differentiable at irrationals?
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
38804
Wrong Wolfram|Alpha limit? $ f(x,y) = \frac {xy}{|x|+|y|} $ for $(x,y)\to(0,0)$
142870
Prove the function is not differentiable at (0,0)
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
117770
Let $\displaystyle f$ be differentiable, $\displaystyle f(x)=0$ for $|x| \geq 10 $ and $g(x)=\sum_{k \in \mathbb Z}f(x+k).$
151575
Differentiable bijection $f:\mathbb{R} \to \mathbb{R}$ with nonzero derivative whose inverse is not differentiable
144013
If $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.
16375
Is the function differentiable at $0$?
93528
Continuous versus differentiable