Understanding the Chain Rule
The chain rule is a fundamental theorem in calculus used for differentiating compositions of functions. It states:
If a function y = f(g(x)), then the derivative dy/dx = f'(g(x)) * g'(x).
Why is it Useful? 🤔
When dealing with complex functions, the chain rule allows us to break down the problem into simpler parts, making differentiation more manageable.
Example 📝
Consider the function y = (3x + 2)^4. Let u = 3x + 2, then y = u^4. Differentiating:
- dy/du = 4u^3
- du/dx = 3
Hence, dy/dx = 4u^3 * 3 = 12(3x + 2)^3.
