CAIE A-Level Mathematics 1.7.2 Differentiation Rules

CAIE A-Level Mathematics 1.7.2 Differentiation Rules
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise differentiating rational powers, sums and composite expressions with the power and chain rules and simplifying first or second derivatives before substitution.

How this is tested

  • multiply by the original power, reduce the exponent by one and retain constant factors
  • differentiate a composite bracket by multiplying by the derivative of its inner function
  • differentiate again or substitute the stated x-value to find the rate of change of gradient

Question 11(b)

[Maximum number: 3]

A curve passes through the point P(4,3) and is such that

dy dx=8x2−10(2x−3)2.\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{8}{x^{2}}-\frac{10}{(2 x-3)^{2}} .

Find the rate of change of the gradient of the curve when x=4.