Techniques of Differentiation — Single-Variable Calculus

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.

$ 8.58

Payment required for enrolment
Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
[FUTA, Akure] MTS 102: Introductory Mathematics II
[FUTA, Akure] MTS 102: Introductory Mathematics II
This learning track is structured for first-year students at the Federal University of Technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline. You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time. If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.

This learning track is structured for first-year students at the Federal University of Technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline. You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time. If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.

[UNILAG, Akoka] MTH 102: Elementary Mathematics II
[UNILAG, Akoka] MTH 102: Elementary Mathematics II
This learning track is designed to guide first-year students at the University of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.

This learning track is designed to guide first-year students at the University of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.

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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