3.4 Differentiation

3 of 3 objectives have lessons · 0 studied · 0 secure

Lessons

The P3 derivative setSix new standard derivatives — e^x, ln x, sin x, cos x, tan x and arctan x — plus the chain rule to handle any bracket around them. 8 min, not started
Products and quotients: when two functions are combinedWhen two functions are multiplied, the derivative is not the product of the derivatives — the product rule and quotient rule handle the mixing. 8 min, not started
Implicit differentiation: when y cannot be freedCurves like x² + y² = xy + 7 mix x and y. Differentiate term by term and let dy/dx ride along as an unknown. 8 min, not started
Parametric differentiation: both coordinates ride on tWhen x and y are both functions of t, divide the two derivative rates and t cancels — leaving the curve's gradient at any point. 8 min, not started

3 objectives

What Cambridge says you should be able to do, in our words. Codes are the topic number plus the objective’s position.

3.4.1

Use the derivatives of eˣ, ln x, sin x, cos x, tan x and tan⁻¹x, together with constant multiples, sums, differences and composites.

The derivatives of sin⁻¹x and cos⁻¹x are not required.

Taught in: The P3 derivative set · 6 questions

3.4.2

Differentiate products and quotients.

Examples: (2x − 4)/(3x + 2), x² ln x, x e^(1 − x²).

Taught in: Products and quotients: when two functions are combined · 6 questions

3.4.3

Find and use the first derivative of a function that is defined parametrically or implicitly.

Examples: x = t − e^(2t), y = t + e^(2t); x² + y² = xy + 7. Includes use in problems involving tangents and normals.

Taught in: Implicit differentiation: when y cannot be freed, Parametric differentiation: both coordinates ride on t · 10 questions