Differentiation: power rule

Use it to differentiate any power of x, the starting point for almost every differentiation question.

This formula is not on the exam list, you must memorise it. The printed formula list supplied in the SPM Additional Mathematics paper covers only a specific set of formulae; this is not one of them, so it needs to be secure in your memory before you walk in.

The good news is that formulae like this are used so often that regular practice fixes them naturally, you will rarely need to "revise" a formula you use in every second question. Make it automatic by working problems, not by staring at a list.

The reliable habit with any formula is the same: write the formula first, then substitute, then simplify, each on its own line. That single discipline earns method marks even when the arithmetic slips, because SPM marking is analytic and a marker can see the correct approach.

Before substituting, check you have matched each symbol to the right quantity in the question, and mind the details that quietly cost marks, a sign, a unit, an angle mode on the calculator, a condition on the values. When your answer is out, resist re-reading the whole solution; instead check the substitution line first, which is where most errors actually live.

A formula only becomes useful once you have used it inside real questions, so the best practice is not to drill the formula in isolation but to meet it where the exam puts it, as one step inside a longer problem. Work a handful of questions of rising difficulty that call for Differentiation: power rule, and each time, write the formula, substitute, and simplify as separate lines so the method is visible.

Mark your own work honestly and note any recurring slip. If you find you can state Differentiation: power rule but freeze when a question does not announce that it is needed, that is the real skill to build, recognising the situation, and it is exactly what a one-to-one teacher can rehearse with you using questions tuned to where you are.