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# Lecture 3: Exercises

### Suggestions for further reading

- Differentiation: Bronstein&Semendjajew (chaps. 3.1.5, 3.1.6)

### Questions for Review

- When is a function differentiable?
- How is the derivative of a function defined?
How can the derivative be pictured geometrically?
What are possible notations for the derivative?
- What is the relationship between differentiability and continuity?
Give examples.
- What is a higher derivative? What are possible notations?
- Remember the basic rules for differentiation. In particular,
how do you differentiate
- linear combinations of functions?
- products of functions?
- ratios of functions?
- chains of functions: f(x)=g(h(x))?
- inverse functions?

### Problems