MATSEC AM Pure Mathematics Complete Prep Course — Lesson 62: The derivative as a limit and powers of x

This lesson defines the derivative as the limit, as h tends to zero, of the difference quotient, and identifies that limit as the gradient of the tangent. It differentiates y equals x squared from first principles, then introduces the power rule for every real n, the linearity of differentiation, and the rewriting of roots and reciprocals as powers. Two worked problems cover a first principles proof and a negative power sign trap.

Lesson 62 of 158 in the MATSEC AM Pure Mathematics Complete Prep Course audio course from ExamPrepRise.

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