The Chain Rule
The chain rule is used to differentiate composite functions. If y = f(g(x)), then dy/dx = f'(g(x)) · g'(x).
How to Apply the Chain Rule
- Identify the outer and inner functions
- Differentiate the outer function
- Multiply by the derivative of the inner function
Examples
For y = (3x + 2)^5: outer = u^5, inner = 3x + 2. dy/dx = 5(3x+2)^4 · 3 = 15(3x+2)^4