Hadamard's lemma

Okay kiddo, let's talk about Hadamard's Lemma. Imagine you have a big multiplication problem, like 3 multiply by 4 times 5. To make the problem easier, we can break it down into smaller parts. Hadamard's Lemma is like breaking the big multiplication problem into smaller parts!

Hadamard's Lemma helps us to break down a complicated function into simpler functions. It says that we can take a function that has many variables, and break it down into smaller functions that only have one variable. We do this by taking the partial derivatives of the big function.

Now, what's a partial derivative, you might ask? Let's say you have a function that shows how fast you are running. This function depends on many things, like your speed and how long you have been running. But we only care about how fast you are running at one particular moment, so we only look at one part of the function. That part is called the partial derivative.

So, if we apply Hadamard's Lemma to a function, we end up with a bunch of smaller functions that are easier to work with. This helps us understand the big function better and solve problems more easily.

In summary, Hadamard's Lemma helps us break down a complicated function into smaller, simpler functions by taking partial derivatives. It's like breaking a big multiplication problem into smaller parts to make it easier to solve!