What is the right-hand derivative of this function at x = 1?

Explanation

1. 01

   For $x > 1$, $x\lvert x \rvert = x^{2}$ and $\lvert x - 1 \rvert = x - 1$, so $f(x) = x^{2} + x - 1$.

2. 02

   Its slope at 1 is $2(1) + 1 = 3$.