Derivatives from first principles

Practice derivatives from first principles using the limit definition rather than a list of differentiation rules. Original single-select and multiselect questions develop polynomial expansions, reciprocal subtraction and conjugate rationalization, then test derivative domains and piecewise matching. Worked explanations show the nonzero-increment algebra and the limiting step separately. Pay special attention to excluded denominators, root-domain endpoints and the difference between continuity and differentiability. This optional calculus bridge assumes fluent algebra and an understanding of secant slopes.