Techniques of Differentiation - Single-Variable Calculus (Undergraduate Foundation)
This course builds on your understanding of the derivative by introducing standard differentiation techniques. These include the product rule, quotient rule, and chain rule, as well as derivatives of polynomial, exponential, logarithmic, and trigonometric functions.
You’ll also learn to differentiate composite and implicit functions. The course emphasizes accuracy, pattern recognition, and methodical execution of differentiation steps.
It’s structured to ensure that by the end, finding derivatives becomes second nature.
Enrolment valid for 12 months
Course Chapters
1. Introduction
1. Introduction
Meaning of functions, single-variable real-valued functions, dependent and independent variables, domain of functions.
2. The Derivative
2. The Derivative
Meaning of increments, limits of functions, and the derivative.
3. First-Principle Differentiation
3. First-Principle Differentiation
Differentiation of some general polynomial terms and trigonometric functions from the first principles.
4. Rules of Differentiation
4. Rules of Differentiation
Derivative of a constant, sum and difference of two functions, product and quotient of two functions.
5. Chain Rule
5. Chain Rule
Differentiation of composite functions by the chain rule of differentiation.
6. Implicit Differentiation
6. Implicit Differentiation
Differentiation of implicitly-defined functions.
7. Trigonometric Functions
7. Trigonometric Functions
Differentiation of trigonometric functions.
8. Inverse Trigonometric Functions
8. Inverse Trigonometric Functions
Differentiation of inverse trigonometric functions.
9. Exponential Functions
9. Exponential Functions
Differentiation of exponential functions and its rules.
10. Logarithmic Functions
10. Logarithmic Functions
Differentiation of logarithmic functions and its rules.
11. Parametric Equations
11. Parametric Equations
Differentiation of parametric equations and its rules.
12. Hyperbolic Functions
12. Hyperbolic Functions
Differentiation of hyperbolic functions and its rules.
13. Inverse Hyperbolic Functions
13. Inverse Hyperbolic Functions
Differentiation of Inverse hyperbolic functions, and its rules.
14. Higher Derivatives
14. Higher Derivatives
Successive differentiation and its rules.
15. Applications of Differentiation
15. Applications of Differentiation
Some applications of differentiation of single-variable functions - tangents and normals to curves, curve sketching, maximum and minimum values of functions.