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:
- From those basic formulae are derived these two additional formulae:
- And for exponentials more generally:
- 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 sec, cosec, and cot using the chain rule and the derivatives of the basic trigonometric functions
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
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