(i)[4]
Demonstrate that $\frac{dy}{dx} = \frac{y}{x(3y^3 - 1)}$.
(ii)[4]
Determine the coordinates of the point at which the tangent to the curve is parallel to the $y$-axis, with each coordinate correct to $3$ significant figures.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve is given by the equation $\ln(xy) - y^3 = 1$.
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This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Give or indicate $\frac{1}{x}+\frac{1}{y}\frac{dy}{dx}$ as the derivative of $\ln(xy)$” …
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