A LevelMathsEdexcelPureRevision NotesDifferentiationFurther DifferentiationDifferentiating Other Functions

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

Exam code: 9MA0

Written by: Roger B

Reviewed by: Dan Finlay

Updated on 2 July 2026

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

Differentiating other functions

How do I differentiate common functions?

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

Examiner Tips and Tricks

Worked Example

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Roger B

Reviewer: Dan Finlay

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

Differentiating other functions

How do I differentiate common functions?

How do I differentiate ekx, ax, ln(kx) and akx?

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Roger B

Reviewer: Dan Finlay

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