Is the function $(x^2+y^2)\sin\frac{1}{x^4+y^4}$ differentiable at point $(0,0)$
57407
Show that $(x^2 + y^2) \sin\left(\frac{1}{x^2 + y^2}\right)$ is differentiable.
30533
Showing that this function is infinitely differentiable
112898
Derivative of sin(x)/x at $0$ by definition of derivative
93436
What is the gradient of $f(x, y, z) = \sqrt{x^2+y^2+z^2}$?
31685
Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
8659
How do you show that $e^{-1/x^2}$ is differentiable at $0$?
30855
Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.
87743
Is a function whose derivative vanishes at rationals constant?
71260
Check differentiability of multivariable functions
85480
Let $f(x,y)=\frac{x^3-y^3}{x^2+y^2}$. Is f differentiable in $(0,0)$?
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
10068
$f(x,y)= e^{-\frac{1}{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and $f(0,0)=0$.
72278
What is the value of $\frac{\sin x}x$ at $x=0$?
73786
Limit of $\frac{\sin(x+y)}{x+y}$ as $(x,y) \to (0,0)$
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
6417
Can a function be differentiable at the end points of its (closed interval) domain?