Explanation: f(x)=x|x|,x∈R is differentiable. ={

x2≥0

−x2,‌x<0

if x≠0,
then the function is quadratic so is differentiable.
The only point to consider is 0 . But since both x2 and −x2 have same derivative at 0 , then it follows that f is differentiable at 0 .