AQA A Level Maths: Pure复习笔记7.3.6 Differentiating Reciprocal and Inverse Trig Functions

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

7.3.6-Diff-Rec-Inv-Trig-Illustr-1

How do I differentiate the inverse trigonometric functions?

  • The formulae for the derivatives of the inverse trigonometric functions are:
  • 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 functions7.3.6-Diff-Rec-Inv-Trig-Illustr-3

Exam Tip

  • 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

7.3.6-Diff-Rec-Inv-Trig-Example

 

 

 

 

 

 

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