| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | January |
| Marks | 4 |
| Topic | Differentiation from First Principles |
| Type | First principles: x³ terms |
| Difficulty | Moderate -0.5 This is a standard first-principles differentiation question requiring the limit definition and algebraic manipulation of (x+h)³. While it requires careful algebra with the binomial expansion and cancellation, it's a routine textbook exercise with well-established steps, making it slightly easier than average for A-level. |
| Spec | 1.07g Differentiation from first principles: for small positive integer powers of x |
5. Prove, from first principles, that the derivative of $x ^ { 3 }$ is $3 x ^ { 2 }$\\[0pt]
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\hfill \mbox{\textit{SPS SPS SM 2022 Q5 [4]}}