This course covers determining derivatives through topics such as logarithmic differentiation, derivative rules, implicit differentiation, and trigonometric functions. The learning outcomes include understanding the derivative as a function, applying various derivative rules, and solving derivative problems involving trigonometric and exponential functions. The course teaches skills such as using the power, product, quotient, and chain rules to find derivatives, as well as applying implicit differentiation and logarithmic differentiation. The teaching method includes theoretical explanations, examples, and problem-solving demonstrations. The intended audience for this course is individuals interested in calculus, particularly those looking to deepen their understanding of derivatives and their applications.
Overview
Syllabus
Logarithmic Differentiation.
Derivative of a^x.
Derivative: Sum/Difference Rule.
17th derivative of sin(x).
Rate of Change & Tangent Line.
Derivative of sin(x).
Limit Definition of Derivative.
The Derivative as a Function.
Derivative of ln(x).
Intro to Implicit Differentiation.
Motivating Chain Rule.
Derivative of Square Root.
Derivative of Arcsine.
Second Derivative Using Implicit Differentiation.
Derivative: Power Rule.
Derivatives of Inverse Trig Functions.
Derivative of e^x.
Derivative of tan(x) -- and the other trig functions.
Derivative: Product Rule.
Justifying the Chain Rule.
Chain Rule Examples.
Implicit Differentiation Example.
Derivative: Quotient Rule.
Trig derivative example.
Derivative Example Requiring Both Quotient and Product Rule.
Taught by
math at andrews
