Partial Derivatives and Gradient Descent

What You'll Cover Today

Day 2 of Calculus for AI in 5 Days builds directly on Day 1. You're moving from theory into applied practice. The concepts today require the foundation from yesterday, so if anything felt unclear, review it now.

chain rule

Understanding chain rule is the core goal of Day 2. The concept is straightforward once you see it in practice — most confusion comes from skipping the mental model and jumping straight to implementation. Start with the model, then write the code.

# chain rule — Working Example
# Study this pattern carefully before writing your own version

class chainruleExample:
    """
    Demonstrates core chain rule concepts.
    Replace placeholder values with your real implementation.
    """
    
    def __init__(self, config: dict):
        self.config = config
        self._validate()
    
    def _validate(self):
        required = ['name', 'type']
        for field in required:
            if field not in self.config:
                raise ValueError(f"Missing required field: {field}")
    
    def process(self) -> dict:
        # Core logic goes here
        result = {
            'status': 'success',
            'topic': 'chain rule',
            'data': self.config
        }
        return result


# Usage
example = chainruleExample({
    'name': 'my-implementation',
    'type': 'chain rule'
})
output = example.process()
print(output)

composite functions

composite functions is the practical application of chain rule in real projects. Once you understand the underlying model, composite functions becomes the natural next step.

Jacobian

Jacobian rounds out today's lesson. It connects chain rule and composite functions into a complete picture. You'll use all three concepts together in the exercise below.

Common Mistakes on Day 2

• Skipping the fundamentals — chain rule requires understanding the underlying model before you can apply it correctly. Read the section twice if needed.
• Ignoring error messages — error messages for composite functions are usually precise. Read them carefully before searching online.
• Hard-coding values — anything that might change between environments belongs in configuration, not in your source code.
• Not testing edge cases — the happy path is not enough. What happens with empty input? With unexpected types? With network failures?