Differential Calculus

Eddie Woo via YouTube

Start learning Write review

Learn differential calculus through comprehensive video lessons covering derivatives of trigonometric, exponential, and logarithmic functions with practical applications. Master the fundamental techniques of differentiation including first principles, chain rule, product rule, and quotient rule while exploring derivatives of sine, cosine, tangent, natural logarithm, and exponential functions with various bases. Develop skills in finding tangent and normal equations, analyzing continuity and differentiability, and solving coordinate geometry problems using calculus methods. Practice with real-world applications including turning points, intercepts, and curve sketching for exponential products and trigonometric functions. Build intuitive understanding through visual approaches and step-by-step proofs, progressing from basic derivative rules to complex examples involving composite functions like x^x and a^(cos x). Strengthen problem-solving abilities with exam review sessions and worked examples from advanced mathematics assessments, ensuring thorough preparation for calculus applications in higher-level mathematics.

Syllabus

Find a tangent's equation
Derivatives of 6 Trigonometric Functions
Determining Derivatives for cos(x) & tan(x)
Differentiability (includes counter-examples)
Differentiating sin(x) from First Principles
Interesting Discontinuity Example
Intuitive Approach to Gradient Function of sin(x)
Differentiating Trigonometric Functions - examples
Differentiating Exponential Functions (Computer Aided)
Differentiating Exponential Functions (First Principles)
Differentiating Exponential Functions: e
Differentiating Logarithmic Functions
Differentiating Logarithmic Functions (Examples)
Differentiating x to the power of x
Differentiating a^(cos x)
Differentiating Logarithmic Functions Without Base e
3 Approaches for Co-ordinate Geometry Question
Understanding Exponential Functions and their Gradients: First Principles Approach
Understanding Exponential Functions and their Gradients: Intuitive Approach
The Derivative of ln x
Differentiating Log Functions w/ Chain Rule
Summarising Derivatives of all Trigonometric Functions
Differentiating 2^(5x)
Differentiating Exponential Functions (1 of 3: A Visual Argument for the Derivative)
Differentiating Exponential Functions (2 of 3: Dealing with Any Base)
Differentiating Exponential Functions (3 of 3: Chain Rule)
Differentiating x^x (1 of 3: Reviewing Derivatives of Exponentials & Logarithms)
Establishing the Derivative of ln(x)
Differentiating x^x (2 of 3: By Changing the Base)
Harder Examples & Further Applications (Using 'u' to simplify differentiating exp/log functions)
Calculus of Exponential Products (1 of 3: Finding the Intercepts and Turning Points)
Calculus of Exponential Products (2 of 3: Comparing the Behaviour at the extremities to find POIs)
Calculus of Exponential Products (3 of 3: Using the insight from previous parts to sketch function)
Derivative of natural logarithmic functions (Discovering the connections between each)
Calculus of Trigonometric Functions (1 of 2: Using First Principles to find d/dx of sinx)
Calculus of Trigonometric Functions (2 of 2: Using derivative of sinx and cos x to find d/dx(tanx))
Application of Differentiating Trig Functions (2 of 2: Tangents and normals of a trig function)
Applications of Differentiating Trig Functions (1 of 2: How is differentiating used in maths?)
Maths Test Review (1 of 2: Differentiating a product with a log function)
Chain Rule (1 of 3: Introducing a substitution)
Chain Rule (2 of 3: Combining derivatives)
Chain Rule (3 of 3: Proving a circle property)
Finding a Normal to a Rational Function
What is continuity?
Differentiating Exponentials with Non-e Bases
Calculus of Logarithmic Functions (1 of 4: Introduction)
Calculus of Logarithmic Functions (2 of 4: Establishing the derivative of ln x)
Calculus of Logarithmic Functions (3 of 4: Dealing with non-e bases)
Calculus of Logarithmic Functions (4 of 4: The importance of simplifying first)
Calculus of Trigonometric Functions (1 of 3: Using visual intuition)
Calculus of Trigonometric Functions (2 of 3: An alternative version of first principles)
Calculus of Trigonometric Functions (3 of 3: Proving the basic derivative)
Differentiating Trigonometric Functions (1 of 2: Key results & chain rule)
Differentiating Trigonometric Functions (2 of 2: Example using quotient rule)
Using Derivatives of Trigonometric Functions (1 of 2: Finding a tangent)
Introducing Calculus of Exponential Functions (1 of 6: Considering other functions)
Introducing Calculus of Exponential Functions (2 of 6: Characteristics of the gradient)
Introducing Calculus of Exponential Functions (3 of 6: Using the uniqueness of e)
Introducing Calculus of Exponential Functions (4 of 6: Simple chain rule examples)
Introducing Calculus of Exponential Functions (5 of 6: Common mistakes with notation)
Introducing Calculus of Exponential Functions (6 of 6: Finding equation of a tangent)
Intro to Trigonometric Calculus (1 of 5: Review questions)
Intro to Trigonometric Calculus (2 of 5: Investigating the gradient of sin x)
Intro to Trigonometric Calculus (3 of 5: Investigating gradient magnitude)
Intro to Trigonometric Calculus (4 of 5: Derivative of cos x)
Intro to Trigonometric Calculus (5 of 5: Derivative of tan x)
Differentiating Simple Trigonometric Functions (examples)
Review of Logarithm Laws
Differentiating the Logarithmic Function (1 of 5: Using visual intuition)
Differentiating the Logarithmic Function (2 of 5: Incorporating chain rule)
Differentiating the Logarithmic Function (3 of 5: Proof by implicit differentiation)
Differentiating the Logarithmic Function (4 of 5: Restricting domain)
Differentiating the Logarithmic Function (5 of 5: Equation of a tangent)
Differentiating Exponentials with Other Bases (1 of 3: Review questions)
Differentiating Exponentials with Other Bases (2 of 3: Deriving a key result)
Differentiating Exponentials with Other Bases (3 of 3: Establishing the formula)
Differentiating Logarithms with Other Bases
A Turning Point Mystery (1 of 2: Introducing the problem)
A Turning Point Mystery (2 of 2: An unusual derivative)
Differential Calculus Exam Review (3 of 3: Product rule, trigonometric functions)
Differential Calculus Exam Review (2 of 3: Logarithms & exponentials)
Differential Calculus Exam Review (1 of 3: Chain rule)
Differentiating Exponential Functions (1 of 2: Reviewing simple derivatives)
Differentiating Exponential Functions (2 of 2: Step by step Chain Rule)
Differentiating Exponential Functions continued (2 of 2: Further examples)
Exponential Functions with Other Bases (1 of 2: Reframing problems)
Exponential Functions with Other Bases (2 of 2: Deriving the formula)
Differentiating Logarithmic Functions (1 of 4: Developing intuitions)
Differentiating Logarithmic Functions (2 of 4: Proving the formula)
Diffferentiating Logarithmic Functions (3 of 4: Basic examples)
Differentiating Logarithmic Functions (4 of 4: Further examples)
Applications of Differentiating Log Functions (1 of 2: Calculating a tangent)
Applications of Differentiating Log Functions (2 of 2: Calculating a normal)
Differentiating Trigonometric Functions (1 of 5: Review questions)
Differentiating Trigonometric Functions (2 of 5: Taking gradient measurements)
Differentiating Trigonometric Functions (3 of 5: Understanding cos x & tan x)
Differentiating Trigonometric Functions (4 of 5: Chain rule examples)
Differentiating Trigonometric Functions (5 of 5: Exploring the derivative of tan x)
Application of Trigonometric Derivatives (1 of 2: Finding the tangent)
Application of Trigonometric Derivatives (2 of 2: Evaluating an area)
Summary of Exponential, Logarithmic & Trigonometric Derivatives
Question 30 (this year's HSC Mathematics Advanced exam)