Mathematics - Calculus - Differential - Chain rule - The Chain Rule

10 steps: (1) The chain rule handles COMPOSITE functions: f(g(x)). (2) d/dx[f(g(x))] = f'(g(x)) · g'(x). 'Derivative of outer, evaluated at inner, times derivative of inner.' (3) Shortcut: if y=f(u) and u=g(x), then dy/dx = dy/du · du/dx. (4) Example 1: d/dx[(3x+1)⁵]. Outer: u⁵, inner: u=3x+1. Answe