1. The foundation of the derivative -- The derivative of a function at a point -- The derivative as a function -- The Leibniz notation --

2. Using the derivative for powers and linear combinations -- The derivatives of rational powers of x -- The derivatives of linear combinations -- Higher-order derivatives -- The proof of the power rule for arbitrary rational powers --

3. Using the derivatives of sine and cosine -- The derivatives of sine and cosine at 0 -- The derivative functions corresponding to sine and cosine --

4. Using the derivative in velocity and acceleration --

5. Local linear approximations -- The differential -- The traditional notation for the differential -- The accuracy of local linear approximations --

6. Understanding the product and quotient rules -- The quotient rule --

7. Applying the chain rule -- A plausibility argument for the chain rule -- The chain rule in the Leibniz notation -- The chain rule for more than two functions -- The proof of the chain rule --

8. The problems of related rates --

9. The intermediate value theorem -- Newton's method --

10. Using implicit differentiation --

Index.