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This topic differentiates the standard functions — eˣ, ln x, sin x, cos x and tan x — whose derivatives must be known by heart and combine with the chain, product and quotient rules. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Learn the standard derivatives: e to the x stays as itself, ln x gives 1 over x, sin x gives cos x, cos x gives minus sin x. With a function inside, apply the chain rule and multiply by the inner derivative.
Before you start
The groundwork here is basic differentiation and exponentials. Keep it sharp for the chain, product and quotient rules.
What you learn
This lesson establishes each one, extends them to multiples and composites with the chain rule, and then combines them using the product and quotient rules. The course works through combining with the rules. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Standard Functions is a Differentiation topic in the A-level syllabus, covered here at the second year of A-level. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Nearby topics in the same strand are Tangents & Normals, Basic Differentiation, Chain Rule and Connected Rates of Change. For unlimited practice, the Differentiation revision engine builds new questions on demand and records your accuracy.
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