CAIE A-Level Mathematics 2.4.3 Implicit and Parametric Differentiation

CAIE A-Level Mathematics 2.4.3 Implicit and Parametric Differentiation
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise differentiating implicitly or parametrically, isolating dy/dx and using its value or sign to calculate gradients, tangents, normals and monotonic behaviour.

How this is tested

  • differentiate every y-term implicitly with a dy/dx factor and collect those terms
  • calculate dx/dt and dy/dt separately before forming dy/dx = (dy/dt)/(dx/dt)
  • substitute the stated point or parameter and use the gradient for a tangent, normal or sign test

Question 6(b)

[Maximum number: 6]

A curve has equation (x2−3)ln⁡y+6x=14\left(x^{2}-3\right) \ln y+6 x=14.

Find the equation of the tangent to the curve at the point (2,e2)\left(2, \mathrm{e}^{2}\right). Give your answer in the form y=m x+c, where m and c are exact constants.