Calculus
Differentiation: definition and basic derivative rules
- Defining average and instantaneous rates of change at a point
- Defining the derivative of a function and using derivative notation
- Estimating derivatives of a function at a point
- Connecting differentiability and continuity: determining when derivatives do and do not exist
- Applying the power rule
- Derivative rules: constant, sum, difference, and constant multiple: introduction
- Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule
- Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)
- The product rule
- The quotient rule
- Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions
Register for a session to review this topic with a small group of learners.
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
We will review the unit topics and go through a few practice questions together. Learners will also have an opportunity to ask any question they may have.
MB
Mohamed Ilyas B
0
2/15
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
We will cover the product rule (explanation and practice)
MB
Mohamed Ilyas B
0
5/10
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
We will cover the quotient rule (explanation and practice)
MB
Mohamed Ilyas B
0
5/10
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Rates of Change
Derivative of a Function using the limit definition
Tangent & Normal Lines
SL
HL
Hyemin L
0
9/30
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Introduction to Differentiation: Understand the concept of differentiation, its geometric meaning, and its fundamental role in analyzing change.
SL
BS
Benyamin S
0
9/12
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Basic Rules of Differentiation: Learn essential rules, including the power, constant, and sum/difference rules, to calculate derivatives efficiently.
SL
BS
Benyamin S
0
9/12
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Today we will define Differentiation. Before calculus, there was no way to find the slope at a particular value, however using the concept of a limit, it is possible to make sense of this. The derivative has numerous applications in business and finance, physics, and many other areas, as we will see later in this course.
BL
NB
Noah B
0
7/30
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
The Chain Rule
The Product & Quotient Rule
SL
HL
Hyemin L
0
9/30
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
The Second and Higher Order Derivatives
Implicit Differentiation
SL
HL
Hyemin L
0
9/30
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Product and Quotient Rules: Master the techniques for finding derivatives of products and quotients of functions with precision.
SL
BS
Benyamin S
0
9/12
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Kinematics (velocity, acceleration, etc.)
Other rates of change (cost function in economics, etc.)
SL
HL
Hyemin L
0
9/30
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Implicit Differentiation: Discover how to differentiate equations where variables are intertwined, introducing a powerful tool for solving complex problems.
SL
BS
Benyamin S
0
9/12
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Higher-Order Derivatives: Analyze second and higher-order derivatives to understand acceleration, concavity, and other advanced concepts.
SL
BS
Benyamin S
0
9/12
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Applications of Differentiation: Apply differentiation to real-world problems, including optimization, related rates, and curve sketching.
SL
BS
Benyamin S
0
9/12
Dr
Calculus · series session
Differentiation: definition and basic derivative rules
Differentiation Review and Problem Solving: Reinforce all differentiation techniques and tackle a wide range of challenging problems in a final review session.
SL
BS
Benyamin S
0
9/12
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