Physical, Mathematical, Computer and Life Sciences › Mathematical Sciences
Derivatives of Functions and Their Applications Training
Description
This course equips learners with the skills to find derivatives of a range of functions, including polynomial, exponential, logarithmic, and trigonometric functions, and apply these techniques to solve real-world problems. Learners will develop the ability to analyze and interpret rates of change, optimize functions, and model dynamic systems, enhancing their analytical and problem-solving capabilities in technical and business contexts.
Learning Outcomes
- Apply differentiation rules to find derivatives of polynomial, exponential, logarithmic, and trigonometric functions.
- Analyze functions using derivatives to determine critical points, intervals of increase/decrease, and concavity.
- Evaluate real-world problems involving rates of change, such as velocity and acceleration, using derivatives.
- Implement optimization techniques to solve problems involving maxima and minima in business and engineering contexts.
- Demonstrate the use of derivatives in modeling and interpreting dynamic systems.
- Apply the chain rule, product rule, and quotient rule to differentiate composite, product, and quotient functions.
Target Audience
This course is designed for professionals, technicians, and students in engineering, finance, data science, and related fields who need to apply calculus concepts to solve practical problems. It is also suitable for anyone seeking to strengthen their mathematical foundation for further study or career advancement.
Prerequisites
None — open enrollment. However, a basic understanding of algebra and functions is recommended.
Course Outline
Objectives:
• Understand the concept of a derivative as a rate of change.
• Apply the definition of the derivative to find derivatives from first principles.
• Use basic differentiation rules (power, constant, sum/difference).
• Differentiate polynomial functions.
Topics:
• Introduction to limits and continuity.
• Definition of the derivative and its geometric interpretation (slope of tangent).
• Differentiation from first principles.
• Basic differentiation rules: constant, power, constant multiple, sum/difference.
• Differentiating polynomial functions.
• Examples and exercises on basic differentiation.
Objectives:
• Apply the product, quotient, and chain rules.
• Differentiate exponential and logarithmic functions.
• Differentiate trigonometric functions.
• Use implicit differentiation for equations not solved for y.
Topics:
• Product rule and quotient rule.
• Chain rule for composite functions.
• Derivatives of exponential and logarithmic functions.
• Derivatives of trigonometric functions (sin, cos, tan).
• Implicit differentiation.
• Higher-order derivatives.
• Examples and exercises on advanced techniques.
Objectives:
• Use derivatives to find rates of change in real-world contexts.
• Apply the first and second derivative tests to determine increasing/decreasing intervals and concavity.
• Solve optimization problems.
• Interpret derivatives in business and economic contexts (marginal analysis).
Topics:
• Rates of change in science and engineering.
• Increasing and decreasing functions; first derivative test.
• Concavity and points of inflection; second derivative test.
• Optimization problems (maxima and minima).
• Marginal cost, revenue, and profit in economics.
• Related rates problems.
• Summary and review.
Practicals
Overview
Practical sessions reinforce differentiation skills through hands-on problem-solving and real-world applications. Learners work on worksheets, use graphing software to visualize derivatives, and solve optimization case studies.
Practical Activities
- Basic Differentiation Practice — Learners solve a set of problems on basic differentiation rules, including first principles and polynomial functions. (2h)
- Advanced Rules and Functions — Learners practice product, quotient, chain rules, and differentiate exponential, logarithmic, and trigonometric functions using worksheets and peer collaboration. (3h)
- Applications and Optimization — Learners work on real-world problems: rate of change, curve sketching, and optimization. They use graphing calculators or software to verify results. (3h)
Summatives
Each delegate is assessed continuously throughout the course via daily exercises, scored practical assignments, and a final summative test at the end.
Practical Assignments — 30%
Practical assignments are observed and scored against a rubric during the practical sessions. Each delegate's practical mark is averaged into a single 100% score and contributes 30% to the final total.
Daily Exercises — 20%
Every training day ends with a multiple-choice exercise scored out of 100%. The scores from each daily exercise are averaged across the duration of the course to produce a Daily Average mark, which contributes 20% to the final total.
Final Test — 50%
On the last day a final summative test is written. It is a multiple-choice paper with multiple-answer questions: each question may have more than one correct option, and a single wrong selection on a question marks the entire question wrong — no partial credit. The final test is scored out of 100% and contributes 50% to the overall mark.
Final Total
| Component | Out of | Weight |
|---|---|---|
| Practical Assignments (rubric-scored) | 100% | 30% |
| Daily Average (multiple choice) | 100% | 20% |
| Final Test (multi-answer multiple choice) | 100% | 50% |
| Final Total | — | 100% |
All marks are recorded on the AATICD LMS and visible to each learner under their account.
Certificate
How it works
- Certificates are auto-generated on the AATICD LMS as soon as the marks pass the 50% threshold.
- Each certificate is a branded PDF with the delegate's name, the course title, the unit standard ID, NQF level, credits, and the date of issue.
- You can download or print your certificate from your LMS dashboard at any time after issue — there's no reissue fee and no expiry date.
- If you scored under 50% you can sit the final test again at the next scheduled session at no extra cost.
Where to find it
Sign in to the LMS, open your dashboard, and your certificates appear under My Certificates. Each entry has a View / Download button and a print option.
Training Discounts
Group discounts apply automatically — the more delegates you enrol, the greater the saving. Discounts are calculated at 3% per 5 delegates, scaling up to 40% off for 100+ delegates.
| Delegates | Discount |
|---|---|
| 5 | 3% off |
| 10 | 6% off |
| 15 | 9% off |
| 20 | 12% off |
| 25 | 15% off |
| 30 | 18% off |
| 50 | 30% off |
| 75 | 40% off |
| 100 | 40% off |
3% discount per 5 delegates, up to 40% off for 100+ delegates. Contact us for a custom group quote.
Let us know you're interested and we'll arrange a session that suits you.
Let us know you're interested and we'll arrange a session that suits you.
Let us know you're interested and we'll arrange a session that suits you.
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