IB Math AI 5.3 - The Power Rule Notes

This IB Maths AI SL 5.3 – The Power Rule (Student Notes) resource provides clear, structured notes to help students build a solid foundation in differentiation. The material introduces the derivative as an instantaneous rate of change and connects the formal definition using limits to the practical power rule for differentiating polynomial functions. Key ideas are presented concisely to support understanding before procedural practice.

The notes guide learners through recognising patterns in derivatives of powers of (x), applying the power rule term-by-term to polynomials, and evaluating derivatives at specific values. Worked examples model the full process, while tips reinforce important ideas such as constants differentiating to zero and factoring derivatives to support later sign analysis. The resource also links derivative results to graphical behaviour, showing how (f’(x)) determines where a function is increasing or decreasing.

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