CIE A Level Maths: Pure 3复习笔记4.1.1 Differentiating Other Functions (Trig, ln & e etc)

Differentiating Other Functions (Trig, ln & e etc)

How do I differentiate common functions?

  • These are the common results

How do I differentiate exponentials and logarithms?

  • The two basic differentiation formulae are:

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

  • From those basic formulae are derived these two additional formulae:

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 exponentials more generally:

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

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 seccosec, 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

Exam Tip

  • All of the above are in the formula book, make sure you know how to find them.
  • They will be particularly useful when working with identities and when integrating trigonometric functions.
  • Recognising the derivative of tan-1x will be particularly useful for integrating some functions.

Worked Example

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

 

 

 

 

 

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