A LevelMathsEdexcelPureRevision NotesDifferentiationFurther DifferentiationDifferentiating Reciprocal and Inverse Trig Functions

Differentiating Reciprocal and Inverse Trig Functions (Edexcel A Level Maths) : Revision Note

Roger B

Author

Roger B

Last updated

Edexcel Maths: PureOCR Maths A: PureAQA Maths: Pure

Did this video help you?

Differentiating Reciprocal and Inverse Trig Functions

How do I differentiate the reciprocal trigonometric functions?

  • The formulae for the derivatives of the reciprocal trigonometric functions are:

fraction numerator d over denominator d x end fraction left parenthesis sec x right parenthesis equals sec x tan x
fraction numerator d over denominator d x end fraction left parenthesis cosec x right parenthesis equals negative cosec x cot x
fraction numerator d over denominator d x end fraction left parenthesis cot x right parenthesis equals negative cosec squared x

  • You can derive the derivatives for sec, cosec, and cot using the chain rule and the derivatives of the basic trigonometric functions 

Diff Rec Inv Trig Illustr 1, AS & A Level Maths revision notes

How do I differentiate the inverse trigonometric functions?

  • The formulae for the derivatives of the inverse trigonometric functions are:

fraction numerator d over denominator d x end fraction left parenthesis arcsin x right parenthesis equals fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction
fraction numerator d over denominator d x end fraction left parenthesis arc cos x right parenthesis equals negative fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction
fraction numerator d over denominator d x end fraction left parenthesis arc tan x right parenthesis equals fraction numerator 1 over denominator 1 plus x squared end fraction

  • You can derive the derivatives of arcsin, arccos, and arctan using the reciprocal form of the chain rule and the derivatives of the basic trigonometric functions

    Diff Rec Inv Trig Illustr 3, AS & A Level Maths revision notes

Examiner Tips and Tricks

  • The formulae for the derivatives of sec x, cosec x, and cot x are in the  formulae booklet – you don't need to memorise them

    • However, you should know how to derive the derivatives of sec, cosec, and cot using the chain rule

  • The formulae for the derivatives of arcsin, arccos, and arctan are not in the formulae booklet

    • You should know how to derive those derivatives using the reciprocal form of the chain rule

Worked Example

Diff Rec Inv Trig Example, AS & A Level Maths revision notes

You've read 1 of your 5 free revision notes this week

Unlock more, it's free!

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

the (exam) results speak for themselves:

  • I would just like to say a massive thank you for putting together such a brilliant, easy to use website.I really think using this site helped me secure my top gradesin science and maths. You really did save my exams! Thank you.

    Beth
    IGCSE Student

  • This website is soooo useful and I can’t ever thank you enough for organising questions by topic like this. Furthermore, the name of the website could not have been more appropriate as it literally did SAVE MY EXAMS!

    Fathima
    A Level Student
Test yourself

Did this page help you?

Previous:Quotient RuleNext:Concave & Convex Functions
Roger B

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.

Download notes on Differentiating Reciprocal and Inverse Trig Functions