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International A Level (IAL)MathsEdexcelPure 3Revision NotesDifferentiationFurther DifferentiationDifferentiating Other Functions

Differentiating Other Functions (Edexcel International A Level (IAL) Maths): Revision Note

Exam code: YMA01

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Last updated

27 June 2025

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Differentiating other functions

How do I differentiate common functions?

These are the common results
- $\frac{d}{d x} (x^{n}) = n x^{n - 1}$
- $\frac{d}{d x} (e^{x}) = e^{x}$
- $\frac{d}{d x} (a^{x}) = a^{x} \ln a$ for $a > 0$
- $\frac{d}{d x} (\ln x) = \frac{1}{x}$
- $\frac{d}{d x} (\sin x) = \cos x$
- $\frac{d}{d x} (\cos x) = - \sin x$
- $\frac{d}{d x} (\tan x) = \sec^{2} x$
- $\frac{d}{d x} (\cot x) = - \cos {ec}^{2} x$
- $\frac{d}{d x} (\sec x) = \sec x \tan x$
- $\frac{d}{d x} (\cos ec x) = - \cos ec x \cot x$

How do I differentiate e^kx, a^x, ln(kx) and a^kx?

Diff Other Funct Illustr 1, AS & A Level Maths revision notes

Diff Other Funct Illustr 2_forms, AS & A Level Maths revision notes

Diff Other Funct Illustr 2_derivs, AS & A Level Maths revision notes

And for a^kx:

Diff Other Funct Illustr 3, AS & A Level Maths revision notes

This last formula can be derived from Formula 3 by using the chain rule

Examiner Tips and Tricks

The formulae for some of these derivatives are not given in the formulae booklet – you need to know them.
The formulae for e^kx and ln x are the ones you absolutely do need to know .
The other formulae can be derived from those two as shown above, and remember – the derivative of ln kx is $\frac{1}{x}$ , NOT $\frac{k}{x}$ !

Worked Example

Diff Other Funct Example, AS & A Level Maths revision notes

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Author: Roger B

Expertise: Maths Content Creator

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.