The Limit Definition of the Derivative Let f(a) = 4x2. Calculate f'(x) by completing the steps below 1. Original Problem Given f(x) = 4x2 find f' (x) 2. Set up, but do not simplify, the difference f' (2) = lim quotient for f(a) 3. Multiply out the numerator to get rid of f'(2) = lim parentheses but do not simplify h -+0 4. Simplify completely but do not take the limit f' (2) = lim h -+0 5. Now take the limit to get your simplified answer f' (z ) = Question Help: Video