Physical, Mathematical, Computer and Life Sciences Mathematical Sciences

Derivatives of Simple and Trigonometric Functions Training

SAQA US 243842 | NQF 4 | Credits 6 | Duration 3 Days
From $713 per delegate

Description

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.

Learning Outcomes

  • Apply differentiation rules to find derivatives of simple algebraic functions.
  • Differentiate trigonometric functions including sine, cosine, and tangent.
  • Apply the chain rule, product rule, and quotient rule to composite functions.
  • Solve optimization and rate-of-change problems using derivatives.
  • Analyze function behaviour (e.g., monotonicity, concavity) using first and second derivatives.
  • Evaluate limits and continuity as prerequisites for differentiation.

Target Audience

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.

Prerequisites

None — open enrollment. However, a basic understanding of algebra and functions is recommended.

Course Outline

Day 1: Foundations of Differentiation

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

Day 2: Derivatives of Trigonometric Functions

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

Day 3: Advanced Applications and Integration

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

Practicals

6 hours of practicals To be conducted online or on-campus or in-house
Overview

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.

Practical Activities
  • Practical 1: Basic Differentiation and Interpretation — Learners solve a set of polynomial derivative problems and plot the original function and its derivative using graphing software to observe slope changes. (2h)
  • Practical 2: Trigonometric Derivatives and Rules — Learners practice product and quotient rules with trigonometric functions, then solve a real-world problem involving oscillatory motion. (2h)
  • Practical 3: Chain Rule and Optimisation Project — Learners work in pairs to solve chain rule problems and complete a mini-project: optimise the dimensions of a container to minimise material cost given volume constraints. (2h)

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

Certificate of Completion

Awarded to delegates who achieve an overall mark of 50% or higher on the Final Total (Practicals 30% + Daily Average 20% + Final Test 50%).

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 35% off
100 40% off

3% discount per 5 delegates, up to 40% off for 100+ delegates. Contact us for a custom group quote.

Upcoming Training Sessions
Online training — attend live sessions from anywhere via our virtual classroom.
No online sessions scheduled yet.
Let us know you're interested and we'll arrange a session that suits you.
Contact Us
On-Campus training — face-to-face sessions at our training venues across Africa and beyond.
No on-campus sessions scheduled yet.
Let us know you're interested and we'll arrange a session that suits you.
Contact Us
In-House training — we bring the trainer to your organisation, tailored to your team.
No in-house sessions scheduled yet.
Let us know you're interested and we'll arrange a session that suits you.
Contact Us
Training Discounts
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% off per 5 delegates, up to 40% for 100+

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