Derivative of Absolute Function | Calculus

Question:

Evaluate the derivative of $|x-3|$ at $x=-1$

Answer:

Writing the function in piecewise form, we get $$f(x)=\{\begin{array}{ll}x-3& x>3\\ 3-x& x\le 3\end{array}$$ For $x=-1$, we only choose the function when $x\le 3$, $$f(-1)=3-(-1)=4$$ $$f^{\prime }(x)=\frac{d}{dx}(3-x)=-1$$ $$f^{\prime }(-1)=-1$$