Free course

Introduction to differentiation

This free course is an introduction to differentiation. Section 1 looks at gradients of graphs and introduces differentiation from first principles. Section 2 looks at finding derivatives of simple functions. Section 3 introduces rates of change by looking at real life situations. Section 4 looks at using the derivative of a function to deduce useful facts for sketching its graph. Section 5 covers the second derivative test, used to determine the nature of stationary points and ends by looking at rates of change, including the real-life situation, using differentiation to find acceleration.

Course learning outcomes

After studying this course, you should be able to:

  • understand the idea of differentiation from first principles
  • differentiate power functions
  • find stationary points of some functions
  • determine the nature of some stationary points using either the first or second derivative tests
  • understand and work with derivatives as rates of change in mathematical models.

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Course content