LCHL Maths – Differentiation

Leaving Cert Higher Level Maths LCHL Maths – Differentiation

LCHL Differentiation

The LCHL Differentiation strand — first principles, the rules of differentiation, and applications like rates of change, tangents and turning points.

Your progress through this topic0 of 21 lessons

Lessons in this topic

All 21 lessons, in order — each one ticks off as you open it.

Key ideas in this topic

From first principles — From first principlesDifferentiation 2

Power rule — Power ruleDifferentiation

Product rule — Product ruleDifferentiation 6

Quotient rule — Quotient ruleDifferentiation 7

Chain rule — Chain ruleDifferentiation 8

Applications you must know

The first derivative = tan of the angle the tangent makes with the horizontal — The first derivative = tan of the angle the tangent makes with the horizontaldy/dx = tan θ (angle with the positive x-axis)

Turning point — Turning pointdy/dx = 0

Point of inflection — Point of inflectiond²y/dx² = 0

Increasing / decreasing — Increasing / decreasingsign of dy/dx

Displacement → velocity → acceleration — Displacement → velocity → accelerationdifferentiate with respect to time

Check it against the exam

Jump straight to the fully worked solution for that paper.

2023 Paper 1 Q5 →2023 Paper 1 Q6 →2023 Paper 1 Q9 →2022 Paper 1 Q10 →2022 Paper 1 Q6 →

Topic Content

0% Complete 0/21 Steps

Differentiation 1 – Introduction

Differentiation 2 – First Principles

Differentiation 3 – Trigonometric Functions

Differentiation 4 – PTA

Differentiation 5 – Exponentials

Differentiation 6 – Product Rule

Differentiation 7 – Quotient Rule

Differentiation 8 – Chain Rule

Differentiation 9 – Logs

Differentiation 10 – Implicit Differentiation

Differentiation 11 – Inverse Trig

Differentiation 12 – Substitution

Differentiation 13 – The Second Derivative

Differentiation 14 – Slopes

Differentiation 15 – Turning points/Maximum and Minimum points

Differentiation 16 – Increasing/ Decreasing Curves

Differentiation 17 – Points of Inflection

Differentiation 18 – Rates of Change (Displacement, Velocity, Acceleration)

Differentiation 19 – Tan of the angle made with the horizontal

Differentiation 20 – Rate Problems

Differentiation 21 – Shapes of derivatives