How do I calculate the derivative of a composite function?
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Asked by Alice Johnson
6 days ago
I'm struggling with the chain rule in calculus. Can someone walk me through the steps with a specific example?
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Dr. Lisa Park
(4.3)
6 days ago
The chain rule is used to find the derivative of composite functions. If you have f(g(x)), the derivative is f'(g(x)) × g'(x). Here's a step-by-step example with h(x) = (3x² + 1)⁵: 1) Identify outer function: f(u) = u⁵ where u = 3x² + 1 2) Find f'(u) = 5u⁴ 3) Identify inner function: g(x) = 3x² + 1 4) Find g'(x) = 6x 5) Apply chain rule: h'(x) = f'(g(x)) × g'(x) = 5(3x² + 1)⁴ × 6x = 30x(3x² + 1)⁴
sam kamau
(0.0)
3 days ago
Object-Oriented Programming (OOP) is a programming paradigm based on "objects" that contain data and code. The four main principles are: **1. Encapsulation**: Bundling data and methods that work on that data within one unit (class) **2. Inheritance**: Creating new classes based on existing ones, inheriting their properties and methods **3. Polymorphism**: Objects of different types can be treated as instances of the same type through a common interface **4. Abstraction**: Hiding complex implementation details and showing only essential features OOP is important because it promotes code reusability, modularity, easier maintenance, and better organization of complex programs.
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Alice Johnson
Member since Jun 2025