1. Find the derivative or differential (including higher-order derivative) of a given function, including implicit function and function derivative determined by parametric equation.

2. Prove related propositions and inequalities by using Rolle theorem, Lagrand theorem, Lagrange mean value theorem and Cauchy mean value theorem, such as? Prove that the open interval has at least a little satisfaction? Or discuss the number of roots of the equation in a given interval.

The proof of this kind of questions often needs to construct auxiliary functions, and the construction of auxiliary functions is skillful, which requires readers to analyze and deduce the necessary auxiliary functions step by step from the conditions given in the questions, and also to start from the conclusions to be proved (or its variants)? Recursive? In addition, the monotonicity judgment of functions and the intermediate value theorem of continuous numbers are often used in proof.

3. Find seven undefined limits with Robida's law.

4. The application of maximum and minimum in geometry, physics and economy. To solve this kind of problem, it is mainly to determine the objective function and constraint conditions, and to determine the discussed interval.

5. Use derivatives to study function behavior, describe function images, and so on.