LCHL Maths – Differentiation

Leaving Cert Higher Level Maths LCHL Maths – Differentiation

LCHL Differentiation

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.

1Introduction2First Principles★ Learn off3Trigonometric Functions4PTA5Exponentials6Product Rule7Quotient Rule8Chain Rule9Logs10Implicit Differentiation11Inverse Trig12Substitution13The Second Derivative14Slopes15Turning points/Maximum and Minimum points16Increasing/ Decreasing Curves17Points of Inflection18Rates of Change (Displacement, Velocity, Acceleration)19Tan of the angle made with the horizontal20Rate Problems21Shapes of derivatives

Key ideas in this topic

📖 In the log tables
From first principles
From first principlesDifferentiation 2
📖 In the log tables
Power rule
Power ruleDifferentiation
📖 In the log tables
Product rule
Product ruleDifferentiation 6
📖 In the log tables
Quotient rule
Quotient ruleDifferentiation 7
📖 In the log tables
Chain rule
Chain ruleDifferentiation 8

Applications you must know

★ Must learn
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)
★ Must learn
Turning point
Turning pointdy/dx = 0
★ Must learn
Point of inflection
Point of inflectiond²y/dx² = 0
★ Must learn
Increasing / decreasing
Increasing / decreasingsign of dy/dx
★ Must learn
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 →

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