First principles: x³ terms

Questions asking students to differentiate from first principles where the function is of the form ax³ (e.g., x³, 3x², ⅓x³)

4 questions · Moderate -0.6

1.07g Differentiation from first principles: for small positive integer powers of x

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Edexcel AS Paper 1 2018 June Q10

4 marks Moderate -0.5

Prove, from first principles, that the derivative of \(x ^ { 3 }\) is \(3 x ^ { 2 }\)

Edexcel PMT Mocks Q3

3 marks Moderate -0.5

3. Given that $$y = \frac { 1 } { 3 } x ^ { 3 }$$ use differentiation from first principle to show that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = x ^ { 2 }$$

Pre-U Pre-U 9794/2 2014 June Q3

4 marks Moderate -0.8

3 Given that \(\mathrm { f } ( x ) = x ^ { 3 }\), use differentiation from first principles to prove that \(\mathrm { f } ^ { \prime } ( x ) = 3 x ^ { 2 }\).

WJEC Unit 1 Specimen Q3

6 marks Moderate -0.5

Given that \(y = x^3\), find \(\frac{dy}{dx}\) from first principles. [6]