Differentiating composite functions with the chain rule, products with the product rule and quotients with the quotient rule, including trigonometric functions.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Most functions you meet are built from others: a sine of a polynomial, a polynomial times a sine, a ratio of two polynomials. Three rules handle them all.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
dy/dx = dy/du × du/dx.
d/dx[f(x)]ⁿ = n[f(x)]ⁿ⁻¹ f′(x).
d/dx(uv) = u v′ + v u′.
d/dx(u/v) = (v u′ − u v′)/v².
d/dx sin(g) = g′ cos g; d/dx cos(g) = −g′ sin g.
Product with a chain factor: differentiate each factor with the chain rule.
Factorise and cancel common factors in the answer.
u, v, u′, v′ clearly labelled earns the method mark.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (23 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [12 marks]
Differentiate each of the following with respect to x, simplifying where possible.
(a) y = (3x − 2)⁵ [2]
(b) y = x³ cos 2x [3]
(c) y = (2x + 1)/(x² + 1) [4]
(d) y = √(4x² + 9) [3]
Question 2 [11 marks]
Answer all parts.
(a) Differentiate y = sin²3x and show that dy/dx = 3 sin 6x. [4]
(b) Differentiate y = (x² + 1)/(x − 1). [3]
(c) Find the coordinates of the stationary points of y = x²/(x − 2). [4]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.