Manim Code

Here's the improved prompt:

"Your task is to write a detailed Manim code script that visually explains the chain rule for derivatives to a student who is just learning calculus for the first time.

The animation should:

• Clearly define what the chain rule is in simple, non-technical terms
• Use colorful graphics and moving objects to illustrate the concept
• Break down the chain rule into its component parts and show how they are applied
• Provide a step-by-step walkthrough of the process using a concrete example (e.g., calculating the derivative of sin(x^2))

The script should:

• Be well-commented for clarity
• Include timestamps for each step of the explanation
• Be organized with clear section headers (Introduction, Basic Concept, Chain Rule Demonstration, Example Application)
• Be no longer than 150 lines of code to keep it focused and easy to follow

Assume that the student has a basic understanding of derivatives and the rules for differentiating common functions, but needs clear guidance on how to handle compositions of functions.

Please format your response as a code block with the Manim code and provide a brief summary of what each section of the code does in the response text below the code block.

Thank you for your help in creating this educational resource."