Basic Derivatives - Intro

In this math unit, learners progressively develop skills in calculating derivatives, specifically focusing on functions with negative and fractional powers. Starting with the basics, students first grasp that the derivative of a constant function is zero. They then advance to applying the power rule to find derivatives for negative integer powers and later, negative fractional powers of functions. This skill development is further expanded as learners tackle functions with coefficients, applying the power rule to functions presented as \( f(x) = ax^n \) where \( n \) is a negative integer or a negative fraction. As the unit progresses, complexity increases as they manage negative powers represented as division, further enhancing their understanding of how the power rule applies to functions where variables are in the denominator. This systematic approach builds solid proficiency in handling various forms of power expressions in calculus, essential for comprehending rate changes and derivative calculations.Skills you will learn include:

• The power rule
• Derivative of a constant
• Derivatives of positive and negative powers
• Derivatives of fractional powers
• Derivatives with coefficients