Physical, Mathematical, Computer and Life Sciences › Mathematical Sciences
This course equips learners with the skills to differentiate simple functions and trigonometric functions, and apply these derivatives to solve real-world problems. It builds a strong foundation in calculus, essential for fields such as engineering, physics, and data analysis.
This course is designed for professionals and students in technical fields who need to apply differentiation techniques in their work or studies, including engineers, scientists, and data analysts.
None — open enrollment. However, a basic understanding of algebra and functions is recommended.
Objectives:
• Understand the concept of the derivative as a rate of change
• Apply the power rule to find derivatives of simple polynomial functions
• Differentiate constant multiples and sums of functions
• Solve basic differentiation problems using limit definition
• Interpret the derivative as the slope of a tangent line
Topics:
• Introduction to limits and continuity
• Definition of the derivative
• The power rule for derivatives
• Derivative of constant functions
• Sum and difference rules
• Constant multiple rule
• Graphical interpretation of derivatives
• Worked examples and practice problems
Objectives:
• Derive the derivatives of sine and cosine functions
• Apply the product and quotient rules with trigonometric functions
• Differentiate tangent, cotangent, secant, and cosecant functions
• Combine trigonometric derivatives with polynomial derivatives
• Solve problems involving rates of change in trigonometric contexts
Topics:
• Review of trigonometric functions and their graphs
• Derivative of sin(x) and cos(x) from first principles
• Derivatives of tan(x), cot(x), sec(x), csc(x)
• The product rule for derivatives
• The quotient rule for derivatives
• Chain rule introduction (simple cases)
• Examples with trigonometric and polynomial combinations
• Applications to real-world problems
Objectives:
• Apply the chain rule to composite functions involving trigonometric functions
• Solve higher-order derivatives
• Use derivatives to find maxima, minima, and points of inflection
• Combine differentiation techniques in complex problems
• Integrate differentiation skills in practical problem-solving scenarios
Topics:
• Chain rule for composite functions
• Implicit differentiation (brief introduction)
• Higher-order derivatives
• Applications: curve sketching and optimization
• Related rates problems
• Mixed practice with polynomial and trigonometric derivatives
• Review and assessment preparation
• Course summary and Q&A
Practical sessions reinforce theoretical concepts through hands-on problem-solving, graphing, and real-world applications. Learners will work in groups to solve derivative problems, use graphing software to visualise derivatives, and complete a mini-project applying derivatives to optimisation.
Each delegate is assessed continuously throughout the course via daily exercises, scored practical assignments, and a final summative test at the end.
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.
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.
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.
| 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.
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.
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 | 35% off |
| 100 | 40% off |
3% discount per 5 delegates, up to 40% off for 100+ delegates. Contact us for a custom group quote.
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