Why do all directional derivatives in $0$ exist for $f(x)=\frac{x_1^2x_2}{x_1^2+x_2^2}$?
26602
Continuity and existence of directional derivatives at all directions of a $f:\mathbb{R}^{2} \to \mathbb{R}$ given by $f(x,y)=\frac{2x^2y}{x^2+y^2}$
135941
Derivative of $|x|^\alpha$
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
39995
Showing that partial derivatives of $f(x) = \frac{xy}{x^2+y^2}$ exist for $(x,y) \neq (0,0)$
148737
Is $|xy|$ differentiable in $(0,0)$?
78753
$f(x,y)=4x^3y^2$ Dealing with Directional Derivatives and Vectors
69845
Construct a real function with is exactly $C^2$ such that its first derivative does not vanish everywhere
83301
Intuition behind directional derivative (geometrically)?
100866
Why is $\int_{0}^{\infty} \frac {\ln x}{1+x^2} \mathrm{d}x =0$?
108593
First order weak derivatives of $f(x)=|x|^r$
11017
Does existence of partial derivatives implies continuity at a point $(x_0,y_0)$?
127390
Second derivative of a composite function
124499
Where is the error in my proof that all derivatives are continuous?
115635
Differentiability of antiderivative and continuity of derivative
144426
Example of a function $f:\mathbb{R}^2\to\mathbb{R}$ not differentiable at $(0,0)$, but has a directional derivative at $(0,0)$ in all directions
27888
Why is $|x|$ not differentiable at $x=0$?
119869
Entire function and the series of its successive derivatives