Chain Rule & Gradient Descent Explained

Hey everyone, Dhairya here 👋

After diving into the basics of calculus for ML yesterday (derivatives, partial derivatives, gradients), today I took it a step further into how these concepts actually drive learning in ML models.

🔢 What I Learned Today

The Chain Rule – probably the single most important calculus tool in machine learning. It lets us differentiate complex, nested functions. This is the backbone of backpropagation in neural networks.
Example: If f(x)=(3x2+2x)5f(x) = (3x^2 + 2x)^5f(x)=(3x2+2x)5, using the chain rule makes differentiation manageable.
Gradient Descent (Formal Implementation) – yesterday I visualized it, but today I coded it on a cost function (like mean squared error in linear regression). Watching parameters update step-by-step felt like “the math is alive”.
Connection to ML – realized gradient descent is literally how models learn. Each step is just “apply chain rule → compute gradient → update weights.”

🌱 Reflections

Today felt like connecting the abstract math to the practical engine that powers ML. Without the chain rule and gradients, deep learning wouldn’t even exist.

I also noticed: even though gradient descent seems simple, tuning things like learning rate makes or breaks performance. It’s a balance between moving fast vs. overshooting the minimum.

💻 Notebook

I’ve uploaded my Day 4 notebook (covering Chain Rule, Gradient Decent, and their implementation in ML) here:
👉 GitHub Link – Day 4 Notebook

📚 Resources

🎥 YouTube

🌐 Websites

🎯 What’s Next?

For Day 5, I’ll explore Probability & Statistics basics for ML (distributions, mean, variance, and why they matter in data and models).

Excited to dive into the world of randomness tomorrow 🌌

See you then 👋
— Dhairya

Day 4 – Chain Rule & Gradient Descent in Action