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.

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Enrolment valid for 12 months

Course Chapters

1. Introduction

Meaning of functions, single-variable real-valued functions, dependent and independent variables, domain of functions.

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2. The Derivative

Meaning of increments, limits of functions, and the derivative.

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3. First-Principle Differentiation

Differentiation of some general polynomial terms and trigonometric functions from the first principles.

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4. Rules of Differentiation

Derivative of a constant, sum and difference of two functions, product and quotient of two functions.

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5. Chain Rule

Differentiation of composite functions by the chain rule of differentiation.

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6. Implicit Differentiation

Differentiation of implicitly-defined functions.

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7. Trigonometric Functions

Differentiation of trigonometric functions.

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8. Inverse Trigonometric Functions

Differentiation of inverse trigonometric functions.

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9. Exponential Functions

Differentiation of exponential functions and its rules.

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10. Logarithmic Functions

Differentiation of logarithmic functions and its rules.

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11. Parametric Equations

Differentiation of parametric equations and its rules.

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12. Hyperbolic Functions

Differentiation of hyperbolic functions and its rules.

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13. Inverse Hyperbolic Functions

Differentiation of Inverse hyperbolic functions, and its rules.

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14. Higher Derivatives

Successive differentiation and its rules.

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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.

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