First principles: x² terms

Questions asking students to differentiate from first principles where the function is of the form ax² or ax² + c (e.g., x², 2x², 3x², 5x², 2x²+3)

6 questions · Moderate -1.0

1.07g Differentiation from first principles: for small positive integer powers of x
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Edexcel Paper 1 2024 June Q4
3 marks Moderate -0.8
  1. Given that \(y = x ^ { 2 }\), use differentiation from first principles to show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2 x\)
Edexcel Paper 2 2022 June Q4
3 marks Moderate -0.8
  1. Given that
$$y = 2 x ^ { 2 }$$ use differentiation from first principles to show that $$\frac { \mathrm { d } y } { \mathrm {~d} x } = 4 x$$
OCR MEI Paper 1 2024 June Q6
4 marks Moderate -0.8
6 Given that \(\mathrm { f } ( x ) = 2 x ^ { 2 } + 3\), show from first principles that \(\mathrm { f } ^ { \prime } ( x ) = 4 x\).
AQA Paper 3 2021 June Q3
1 marks Easy -1.8
\(f(x) = 3x^2\) Obtain \(\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\) Circle your answer. [1 mark] \(\frac{3h^2}{h}\) \quad \(x^3\) \quad \(\frac{3(x + h)^2 - 3x^2}{h}\) \quad \(6x\)
Edexcel AS Paper 1 Specimen Q6
4 marks Moderate -0.5
Prove, from first principles, that the derivative of \(3x^2\) is \(6x\). [4]
Edexcel AS Paper 1 Q10
Easy -1.2
Prove, from the first principles, that the derivative of \(5x^2\) is \(10x\).