Introduction to differentiation
Find derivatives using first principles and differentiation rules; apply to tangents, normals and rates of change.
Calculus · MAV-11-06
Sub-topics
Rates of change
Find average rates of change using the secant gradient formula and estimate instantaneous rates of change by evaluating average rates over successively smaller intervals.
The derivative
Find derivatives of monomials and polynomials using the power rule and sum rule, and derive functions from first principles using the limit definition.
Differentiation rules
Differentiate products of functions using the product rule, composite functions using the chain rule, and find equations of tangents and normals to curves.
Applications of the derivative
Determine intervals where a function is increasing or decreasing using the sign of f'(x), find and classify stationary points of polynomials using sign tests, and interpret the derivative in context including position and velocity.