The derivative of $f(x) = x|x|$ at $x = 0$


A. is equal to zero.

B. does not exist because $|x|$ is not differentiable at $x = 0$.

C. does not exist because $f$ is defined piecewise.

D. does not exist because the left and right hand limits do not agree.

In the answer box below, explain your reasoning for the choice you made above. Use complete sentences and correct grammar, spelling, and punctuation. Be specific and detailed. Write as if you were explaining the answer to someone else in class.