I just have a quick, and most likely silly question. I need to show that the function x|--> x|x| is differentiable onR. Would the best way to do this be to let g(x) = x, h(x) = |x|, and use the product rule to show that the derivative is 2x for all x?

Is there anything special I would need to do for x = 0, since |x| isn't differentiable at x=0?

Thanks for your help.