Advanced Derivative Rules - Practice

This math unit guides students through a comprehensive exploration of derivative rules, starting with simple exponential and progressing to complex trigonometric functions. Initially, the focus is placed on mastering derivative calculations for general exponential functions using the general exponential rule combined with the chain rule. As students become proficient with exponential derivatives, the unit introduces increasingly complex scenarios where the exponents contain coefficients, powers, and binomial forms. This progression leads into the application of derivative rules to trigonometric functions, starting with simple angles and gradually moving to more intricate cases involving coefficients, powers, fractions, radicals, and polynomial binomials of angles. The unit intensifies in complexity, teaching students to adeptly manipulate and differentiate functions involving combinations of exponential and trigonometric terms, employing both the trigonometric derivative identities and the chain rule. By the end of the unit, students are expected to efficiently solve advanced calculus problems, reinforcing their understanding of derivative operations particularly in the context of growth, decay models, and trigonometric functions.Skills you will learn include:

• The general exponential rule
• The trigonometric rules
• The chain rule with exponentials and trig functions
• Differentiating exponential and trigonometric functions