Derivatives - Exercises

Here you will find problems for practicing. Each problem has hints coming with it that can help you if you get stuck.
Standard derivatives is something everybody should know, it is a necessary pre-requisite for most calculations in every calculus course. If you are a complete beginner and have troubles with mechanics of differentiation, try to look at Basic methods first.
Typical problems at exams ask about applications of derivative and individual steps related to sketching of functions, here you will find corresponding cathegories. Questions on graphing of functions then pull together all strands of differential calculus.
Not all calculus courses cover implicit and parametric functions; however, they are a must for everyone who wants to looks closer at, say, physics. Here we only touch the basics.

• Calculating derivative: basic methods
• Calculating derivative: standard problems
• Calculating derivative: inverse, implicit and parametric functions
• Tangents and normals, Taylor polynomial and approximation.
• Global extrema and optimization; related rates.
• Applications of MVT: using derivative to compare functions, prove inequalities and count roots.
• Graphing functions: individual basic steps - asymptotes, monotonicity, concavity (for domain and limits see Functions - Exercises).
• Graphing functions
• Implicit and parametric functions