Introduction to Differentiation
Differentiation is one of the most powerful tools in calculus. At its core, it measures the rate of change of a function — telling us how quickly (and in which direction) a function's output changes as its input changes.
The derivative of a function , written or , gives the instantaneous rate of change of at any point . Geometrically, it represents the gradient of the tangent line to the curve at that point.
In SL 5.6, we build our differentiation toolkit with four key techniques:
- The power rule (for polynomials with rational exponents)
- The chain rule (for composite functions)
- The product rule (for products of two functions)
- The quotient rule (for quotients of two functions)
Mastering these rules — and knowing when to combine them — is essential for success in IB DP Analysis & Approaches.
The notation (Leibniz notation) and (Lagrange notation) both mean the same thing: the derivative of (or ) with respect to . The IB uses both — be comfortable with each.