A-level · Differentiation

Implicit differentiationExam-style questions

Finding the gradient of a curve whose equation cannot be rearranged into y = f(x). Why such curves need a new method; differentiating a y-term with the chain rule; products of x and y; collecting dy/dx and why the answer contains both x and y; gradients, tangents and normals at a point; and finding where the tangent is horizontal or vertical.

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40 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
A circle has equation $x^2 + y^2 = 25$ . Find $\dfrac{dy}{dx}$ in terms of $x$ and $y$ , and the gradient at the point $(3, 4)$ .
Level 3 · 3 marksTry it
2
Find $\dfrac{dy}{dx}$ for the curve $x^2 + 3xy + y^2 = 11$ , and the gradient at the point $(1, 2)$ .
Level 3 · 4 marksTry it
3
The curve $C$ has equation $x^2 - xy + y^2 = 7$ . Find the gradient of $C$ at the point $(3, 2)$ .
Level 3 · 4 marksTry it
4
The curve $C$ has equation $x^2 y + x y^2 = 30$ . The point $P(2, 3)$ lies on $C$ . Find the exact gradient of $C$ at $P$ .
Level 3 · 5 marksTry it
5
The circle $C$ has equation $x^{2} + y^{2} = 26$ .

Find the gradient of $C$ at the point $(1, 5)$ . (3 marks)
Level 3 · 3 marksTry it

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