What you will learn:

8.01 Gradient of a curve
8.02 Differentiability
8.03 Differentiation from first principles
8.04 Short methods of differentiation
8.05 Derivatives and indices
8.06 Tangents and normals
8.07 Chain rule
8.08 Product rule
8.09 Quotient rule
8.10 Rates of change

Outcomes:

• understand the derivative of a function as the gradient of the tangent to the curve and a measure of a rate of change
• draw graphs of gradient functions
• identify functions that are continuous and discontinuous, and their differentiability
• differentiate from first principles
• differentiate functions including terms with negative and fractional indices
• use derivatives to find gradients and equations of tangents and normals to curves
• find the derivative of composite functions, products and quotients of functions
• use derivatives to find rates of change, including velocity and acceleration