Explore the fundamental concepts and techniques of calculus in this comprehensive 2.5-hour tutorial on determining derivatives. Master logarithmic differentiation, learn the derivatives of exponential and trigonometric functions, and understand key rules such as the sum/difference, product, quotient, and chain rules. Delve into topics like implicit differentiation, the limit definition of derivatives, and the derivative as a function. Practice with various examples, including higher-order derivatives, rates of change, tangent lines, and derivatives of inverse trigonometric functions. Gain a solid foundation in differentiation techniques essential for advanced mathematical analysis and problem-solving.
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
