Differentiation 1

This introductory calculus topic focuses on the concept of differentiation, the process of finding the rate of change of a function. Learners will explore differentiation rules, applications to curve sketching, and solving problems involving rates and optimization.

Learning Outcomes:
The learner should be able to:

• discuss how the gradient of a curve at a point can be derived from gradient of a chord using small increments.
• Deduce the gradient of the tangent at a point on the curve.
• Understand the concept and notation of differentiation.
• Differentiate basic functions using power, differentiating from first principles and function notations.
• Differentiate between product and quotient functions, composite function, parametric functions, implicit functions.
• Explore second derivatives of functions.
• determine the maximum and minimum values of given functions.
• investigate the nature of turning points in curve sketching and optimization of resources.
• use small changes to approximate roots of numbers, errors in measurements, changes in physical quantities, trigonometric functions.
• Apply differentiation concepts to velocity, displacement and acceleration.
• Solve problems involving rates of change and optimization.
• Use differentiation in practical and theoretical scenarios.