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Determining Derivatives

Offered By: Math at Andrews via YouTube

Tags

Calculus Courses Derivatives Courses Chain Rule Courses Trigonometric Functions Courses Exponential Functions Courses Implicit Differentiation Courses Product Rule Courses Quotient Rule Courses Power Rule Courses

Course Description

Overview

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.

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

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