Okay, I need to create a Wikipedia-style document about composite functions in calculus. Let me start by understanding the user's requirements.

First, the structure: H1 for the title, an overview section, several sections with H2 and H3 headings, and maybe references or related documents. The content needs to be accurate, objective, detailed enough, easy to read, and use technical terms with explanations. Also, markdown formatting with proper hierarchy, lists, tables, emphasis, and code blocks if needed. It should be at least 800 characters.

The main topic is "Composite Functions" under Calculus. Let me recall what composite functions are. A composite function is when you apply one function to the results of another. For example, f(g(x)). I need to explain this clearly.

Start with the title: "복합함수" as given. Then an introduction explaining what they are, their importance in calculus, maybe a simple example.

Next sections could be definitions and notation, properties, examples, applications, and perhaps differentiation rules like the chain rule. Also, maybe common mistakes or tips for students.

I should check if there's any confusion between composite functions and other operations. Make sure to define terms like domain and range in this context. Maybe include a table comparing function composition with other operations.

For the properties section, talk about associativity, identity elements (like the identity function), and how composition works with inverses.

Examples: Use simple functions like f(x) = x² and g(x) = x+1 to show f(g(x)) vs g(f(x)). Maybe a more complex example involving trigonometric or exponential functions.

Applications in calculus could include the chain rule, which is crucial for differentiating composite functions. Explain how the derivative of a composite function is found using the chain rule. Maybe provide an example with differentiation.

Also, mention common mistakes like confusing f(g(x)) with g(f(x)), or mishandling the order of composition.

Need to ensure that technical terms are explained. For instance, when discussing the chain rule, explain what it is and why it's important. Use code blocks if there are any mathematical expressions, but since this is a text document, maybe just use LaTeX notation within the markdown.

Check for clarity: avoid jargon without explanation, keep paragraphs short, use bullet points or numbered lists where appropriate.

Make sure each section flows logically. Start with basics, then move to properties, examples, applications, and common pitfalls.

I should also verify that all information is accurate. For example, the chain rule states that d/dx [f(g(x))] = f’(g(x)) * g’(x). Confirm this.

Include a references section if needed, but since it's a self-contained document, maybe just mention related topics like inverse functions or calculus rules.

Now, structure:

H1: 복합함수

Introduction: Define composite functions, their significance in calculus, and give an example.

Section 1: 정의 및 표기법 (Definitions and Notation) - What is a composite function? - Notation: f(g(x)), sometimes written as (f ∘ g)(x) - Domain considerations: the domain of g must be such that its outputs are within the domain of f.

Section 2: 성질 (Properties) - Associativity: (f ∘ g) ∘ h = f ∘ (g ∘ h) - Identity function: f ∘ id = id ∘ f = f - Inverses: If f and g are inverses, then f(g(x)) = x

Section 3: 예시 및 응용 (Examples and Applications) - Simple examples with polynomials - Trigonometric example: sin(cos(x)) - Application in calculus: chain rule for differentiation

Section 4: 미분과 관련된 규칙 (Differentiation Rules) - Chain Rule explanation - Example of differentiating a composite function

Section 5: 주의사항 및 일반적인 실수 (Common Mistakes and Tips) - Order of composition matters - Misapplying the chain rule - Checking domains when composing functions

References or Related Documents: Maybe mention related topics like inverse functions, calculus rules, etc.

Now, check for markdown formatting. Use H2 for sections, H3 if needed. For example, under "예시 및 응용", have H3 headings for each example type.

Make sure to use proper mathematical notation with LaTeX in the text. Avoid using code blocks unless necessary, but since it's a math document, inline equations are okay.

Check length: 800 characters is about 150-200 words. The user probably meant 800 characters as a minimum, so the actual content should be longer. Need to elaborate each section sufficiently.

Also, ensure that explanations are clear and not too technical without context. For example, when explaining the chain rule, define it step by step.

Now, start drafting each part with these points in mind.