Derivatives

Differentiation rules, techniques, and applications

This section contains 17 topics with 0 subtopics, 77 practice problems and 99 flashcards. Each topic includes comprehensive written notes, worked examples with detailed solutions, and interactive lessons for hands-on practice.

Topics Covered

• The Power Rule — Master the fundamental rule for differentiating polynomial functions
• What is a Derivative? — Understanding the fundamental concept of derivatives
• Derivative Notation — Understanding the different ways to write derivatives
• Derivative as Slope — Understanding derivatives through tangent lines and slope
• Derivative as Rate of Change — Understanding derivatives through real-world rates of change
• The Power Rule — The most fundamental differentiation rule for polynomials
• Constant Multiple and Sum Rules — Essential rules for differentiating linear combinations of functions
• The Product Rule — Differentiating the product of two functions
• The Quotient Rule — Differentiating fractions and rational functions
• The Chain Rule — Finding derivatives of composite functions
• Derivatives of Trigonometric Functions — Finding derivatives of sine, cosine, tangent, and other trig functions
• Derivatives of Exponential Functions — Finding derivatives involving e^x and other exponential functions
• Derivatives of Logarithmic Functions — Finding derivatives involving ln(x) and other logarithmic functions
• Implicit Differentiation — Finding derivatives when y is not isolated
• Related Rates — Finding how rates of change are related to each other
• Higher-Order Derivatives — Second derivatives, third derivatives, and beyond
• Logarithmic Differentiation (Technique) — Using logarithms to simplify difficult differentiation problems

Click on any topic below to start studying.