Find second derivative d²y/dx²

A question is this type if and only if it asks to find the value of the second derivative at a specific point on an implicitly defined curve.

26 questions · Standard +0.8

1.07s Parametric and implicit differentiation
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CAIE Further Paper 2 2024 November Q2
7 marks Standard +0.3
The curve \(C\) has equation $$4y^2 + 4\ln(xy) = 1.$$
  1. Show that, at the point \(\left(2, \frac{1}{2}\right)\) on \(C\), \(\frac{dy}{dx} = -\frac{1}{6}\). [3]
  2. Find the value of \(\frac{d^2y}{dx^2}\) at the point \(\left(2, \frac{1}{2}\right)\). [4]