Fundamentals and Techniques of Differentiation - Calculus (Undergraduate Foundation)

Differentiation measures how quantities change at exact moments. This course builds your complete calculus foundation from first principles to advanced methods. We start with rates of change and formal notation, then cover definitions, continuity, differentiability, and direct proofs. The sequence moves through core rules, composite functions, implicit techniques, parametric systems, and higher-order operations. Each concept links to targeted exercises that test your accuracy before you proceed. These methods solve real problems in physics, engineering, finance, and software development. You will track speed, predict growth, calculate structural stress, and measure market sensitivity. Software developers apply these calculations to optimise machine learning models. Business analysts use them to adjust variables for target profits. The techniques here convert abstract equations into working tools for daily technical tasks. You will calculate derivatives for polynomial, trigonometric, exponential, logarithmic, and hyperbolic functions without reference material. You will apply the product rule, quotient rule, and chain rule to complex expressions. You will perform implicit, parametric, and logarithmic differentiation. You will compute second-order and higher-order derivatives for standard forms. You will verify differential equations through systematic steps. Every lesson forces active practice and precise calculation. The material suits first-year university students, polytechnic learners, and independent learners who require a solid calculus base. Secondary school graduates will gain the exact preparation needed for advanced science and mathematics exams. Technical professionals can use the content to refresh forgotten methods or build reliable calculation habits. The explanations skip heavy theory and focus on working steps. Anyone who handles data, graphs, or mathematical models will apply the methods immediately. You will solve standard calculus problems independently.

22 hrs

$ 11.69

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.
AMS 102: Basic Mathematics
AMS 102: Basic Mathematics
Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings. This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction. You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings. This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction. You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

See more
MTH 102: Elementary Mathematics II - Calculus
MTH 102: Elementary Mathematics II - Calculus
Calculus is the mathematical tool for measuring change and finding the best results in any system. This track follows the official NUC CCMAS MTH 102 curriculum to teach you how functions behave, how to calculate exact rates of change, and how to sum up tiny movements to find total areas or volumes. You will move from basic limits to complex integration techniques used to solve practical problems in the physical world. This track is for first-year university students in engineering, science, and economics departments across Nigeria. It also serves secondary school leavers preparing for technical degrees or university entrance exams. Anyone needing to build a strong foundation in mathematical logic for data analysis or professional licensing will find these lessons essential. After finishing this programme, you will calculate derivatives using first principles and shortcuts, find turning points for optimisation, and solve definite integrals for land measurement or tank design. You will use the trapezium and Simpson's rules to handle experimental data accurately. These skills ensure you pass your university exams and excel in technical careers like civil engineering, physics research, or financial forecasting.

Calculus is the mathematical tool for measuring change and finding the best results in any system. This track follows the official NUC CCMAS MTH 102 curriculum to teach you how functions behave, how to calculate exact rates of change, and how to sum up tiny movements to find total areas or volumes. You will move from basic limits to complex integration techniques used to solve practical problems in the physical world. This track is for first-year university students in engineering, science, and economics departments across Nigeria. It also serves secondary school leavers preparing for technical degrees or university entrance exams. Anyone needing to build a strong foundation in mathematical logic for data analysis or professional licensing will find these lessons essential. After finishing this programme, you will calculate derivatives using first principles and shortcuts, find turning points for optimisation, and solve definite integrals for land measurement or tank design. You will use the trapezium and Simpson's rules to handle experimental data accurately. These skills ensure you pass your university exams and excel in technical careers like civil engineering, physics research, or financial forecasting.

See more

Course Chapters

1. Introduction
7
4
This chapter builds the logic of differentiation from scratch. You will learn why derivatives work before using shortcuts. Mastering these foundations prevents errors in complex calculations later. You will define the derivative via limits, distinguish continuity from differentiability, and prove the power and sine rules. Practical examples cover quadratics, reciprocals, roots, and trig functions.
Concept Overviews
7 Lessons
3:38:37
Problem Walkthroughs
4 Lessons
52:09
2. Fundamental Rules
3
4
Stop using first principles for every sum. This chapter gives you the standard rules to find gradients fast. You will learn to handle constants, powers and roots without stress. These shortcuts save time and reduce errors in complex calculations. They are the basic tools for all future calculus work. You will master the power rule for positive and negative indices; convert roots and fractions into easy powers; apply linearity to split long sums; and simplify algebraic terms before differentiating. These skills let you solve polynomial problems quickly and accurately.
Concept Overviews
3 Lessons
1:03:04
Problem Walkthroughs
4 Lessons
22:22
3. Product and Quotient
2
5
Functions multiplied or divided need special rules. The power rule fails here, so you must learn new techniques to find gradients accurately. Master the product and quotient rules; handle triple products and trigonometric fractions; apply shortcuts for reciprocals; evaluate derivatives at specific points.
Concept Overviews
2 Lessons
1:01:57
Problem Walkthroughs
5 Lessons
27:18
4. Common Derivatives
7
5
This chapter provides standard derivatives for trigonometric, exponential, logarithmic, hyperbolic and absolute value functions. These fixed results allow you to solve routine physics and engineering problems without manual proofs. You will derive key rates from first principles; apply rules to reciprocals and inverses; and handle mixed products. You will memorise standard forms for quick recall during calculations.
Concept Overviews
7 Lessons
2:07:21
Problem Walkthroughs
5 Lessons
29:50
5. Chain Rule
2
7
Functions inside functions require the chain rule. This chapter teaches you to differentiate composite expressions without expanding them, a critical skill for handling complex real-world models in engineering and physics. Master the general formula and derived shortcuts for powers, roots, exponentials, and logs. Learn to combine this with product rules and solve multi-layer trigonometric and inverse trigonometric problems efficiently.
Concept Overviews
2 Lessons
58:54
Problem Walkthroughs
7 Lessons
1:11:40
6. Advanced Techniques
4
6
Standard rules fail for complex curves. This chapter teaches methods for equations where variables are mixed, defined by parameters, or have variable powers. These techniques handle real-world engineering problems that basic algebra cannot solve. You will master implicit differentiation for hidden relationships, parametric gradients for motion, and logarithmic differentiation for variable exponents. Learn to simplify tough expressions using log laws before calculating derivatives.
Concept Overviews
4 Lessons
1:30:01
Problem Walkthroughs
6 Lessons
1:32:46
7. Higher-Order Derivatives
2
6
This chapter measures the rate of change of the gradient. It is vital for calculating acceleration and analysing curvature in engineering and physics. You will move beyond simple slopes to understand how functions behave over successive changes. Master second-order derivatives, successive differentiation, and nth derivative patterns. Learn to handle implicit and parametric forms. Apply these skills to verify solutions for differential equations.
Concept Overviews
2 Lessons
1:00:38
Problem Walkthroughs
6 Lessons
1:26:36
8. Conclusion
1
This chapter consolidates your knowledge of differentiation techniques. It ensures you have the technical foundation needed for the upcoming applications course. You will review the hierarchy of rules, identify the best technique for any function, and confirm mastery of successive differentiation.
Concept Overviews
1 Lesson
14:15