A-Level Calculus Formula Sheet (Differentiation + Integration) | Maths With Faith

A-Level Calculus formula sheet on ONE page ✅
This is my go-to revision sheet for Differentiation + Integration (Edexcel / AQA / OCR).

Differentiation rules included:

• Constants, power rule
• Sum/difference + constant multiple
• Product rule + quotient rule + chain rule
• Exponentials + logs
• Trig derivatives
• Implicit differentiation reminder

Integration rules included:

• Constants + power rule (+C)
• \int \frac{1}{x}dx=\ln|x|+C
• Exponentials + logs
• Trig integrals (sin, cos, sec², csc², sec tan, csc cot)
• Key methods: substitution + by parts
• Definite integrals: F(b)-F(a)

✅ Extra add-ons I included (high-frequency):
• \int \tan x\,dx=\ln|\sec x|+C
• \int \cot x\,dx=\ln|\sin x|+C
• \int \sec x\,dx=\ln|\sec x+\tan x|+C
• \int \cosec x\,dx=\ln|\cosec x-\cot x|+C
• \int \frac{1}{1+x^2}\,dx=\arctan x + C
• \int \frac{1}{\sqrt{1-x^2}}\,dx=\arcsin x + C

📌 Save this for revision.
Comment “DIFF” or “INT” and tell me which topic you want next (product rule / substitution / by parts / implicit).

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