Is $|xy|$ differentiable in $(0,0)$?

multivariable-calculus derivatives

Solution 1:

Hint: $|xy| \le ||(x,y)||^2$...

Related

global error in Euler's method
Symmetric Inequality in $\mathbb{R}$
Integrate $\int \frac{dx}{\sqrt{-ax^2 + bx +c}} $
Basu's theorem to show independence
Expected number of rolls until a number appears $k$ consecutive times
No analytic function in $\{|z|<1\}$ such that $f(0)=1$ and $|f(z)|\ge 1+|z|^2$. Proof strategy
How to get solution matrix from REF matrix
Comparing Differential Entropy of Normal Distribution to Shannon Entropy
Inverse of Linear Transformations
Limit with inverse trignometry [closed]
Does there exist a holomorphic function with the following property?
Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$