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1.7.7 Differentiation from first principles for powers of x

1.7.7 Differentiation from first principles for powers of x

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Question 1

A student tries to differentiate f(x)=kx3f(x)=kx^3f(x)=kx3 from first principles, where k k\,k is a constant. The student writes

f(x+h)−f(x)h=k(x3+3x2h+h3)−kx3h\dfrac{f(x+h)-f(x)}{h}=\dfrac{k(x^3+3x^2h+h^3)-kx^3}{h}hf(x+h)−f(x)​=hk(x3+3x2h+h3)−kx3​.

Identify the error and complete a correct first-principles derivation of f′(x)f'(x)f′(x).

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Markscheme

1.7.7 Differentiation from first principles for powers of x Questions

  1. A Level
  2. /Maths
  3. /1.7.7 Differentiation from first principles for powers of x

8 exam-style questions on OCR A Level Maths 1.7.7 Differentiation from first principles for powers of x. Each one has a worked solution and a mark scheme showing where the marks go.

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