• How derivatives relate to the slope of a function

• How to calculate the derivative of polynomials and special functions

• Differentiation rules for evaluating the derivative of non-trivial functions

• The concept and application of ‘the second derivative’

• How to use differentiation to solve problems in basic motion, mechanics and optimisation.

Week 1: Introduction to differential calculus

• Calculate the derivative of polynomials and functions with real exponents
• Use differentiation to solve a variety of problems including the calculation of slopes of curves, tangents to curves, velocity and acceleration of an object and rate of change of a function
• Use derivatives and second derivatives to find features of functions, including stationary points and inflection points
• Apply the sum, product and quotient rules to find derivatives of simple functions.

Week 2: Differentiation of special functions

• Calculate the derivative of standard trigonometric functions, exponential functions and logarithmic functions
• Apply standard differentiation rules to functions involving trigonometric functions, exponential functions and logarithmic functions.

Week 3: The chain rule

• Recall and apply the chain rule to differentiate composite functions, including those using polynomials, trigonometric functions, exponential functions and logarithmic functions
• Use derivative rules and trigonometric functions, exponential functions and logarithmic functions to solve a variety of problems.

Week 4: Applications of differentiation

• Recall and apply differentiation rules to products, quotients and compositions of functions, including those using polynomials, trigonometric functions, exponential functions and logarithmic functions
• Use derivative rules to derive rules for common special derivatives
• Use derivative rules and trigonometric functions, exponential functions and logarithmic functions to solve a variety of problems.

Week 5: Assessment

There is a timed exam.