So that's the back propagation algorithm and how you compute derivatives of your cost function for a neural network.

So plus f1 of x, that's just the first function, times the derivative of the second function.

You literally just look at this coefficient right here, and you say, OK, well what's half of that coefficient?

When we complete the square, we just take half of this coefficient.

But the application here, at least I don't see the connection.

And this is actually a separable differential equation in and of itself.

So, let's see what this, this equation will do.

Let's do that.

Differentiation

So we could write mu of x is equal to d, the derivative of mu with respect to x, times x.

Well, if we're taking the partial with respect to y here, mu of x, which is only a function of x, it's not a function of y, it's just a constant term, right?

Now let's go to the y terms.

Let's implement this in our code.

In general, the derivative with respect to x of X 2 plus any constant, any constant, is going to be equal to 2X.

Now you add that to the derivative of the second function times the first function.

Modulus

A function that is differentiable everywhere is continuous.

Fine Structure Constant

Here is my solution.

What is a differential equation?

You've already dealt with vectors.

That makes sense, because the separable differential equations are really just implicit derivatives backwards.

If you have a polynomial, you could have more than one values of x that satisfy this equation.

The solution to a differential equation is not a number, it is a function.

And as we see right here, we have the derivative.

And that's true of any sample statistic.

Here we just use our implicit differentiation skills.

Eventually, this capital delta

And if it's an exact equation, that tells us that there exists a psi, such that the derivative of psi of x, y is equal to 0, or psi of x, y is equal to c, is a solution of this equation.

Correlation

Extinction

Cooling factor

The derivative of X 2 is 2X, the derivative with respect to X of pi of a constant is just 0.

So first of all, what is the order of this differential equation?

In total, we are talking about 120 variables in a dynamic system of differential equations.

So I can just rewrite that as A so now A is not a function anymore, it's just a number A times the second derivative of y, with respect to x, plus B times the first derivative, plus C times y.

The first derivative of this expression over here is number 7, and it's interesting it's not number 2.

If psi is a function of x and y, and I would take not a partial derivative, I would take the full derivative of psi with respect to x, it's equal to the partial of psi with respect to x, plus the partial of psi with respect to y, times dy dx.

And I know we did a couple already, but another way to think about separable differential equations is really, all you're doing is implicit differentiation in reverse.

The math teacher explained the concept of partial differentiation.

That's what a differential essentially is.

I expect you to see.

You could rewrite, this is just the derivative of psi, with respect to x, inside the function of x, y, is equal to 0.

So hopefully this gives you a little intuition of why we can just rewrite this equation as the derivative with respect x of psi, which is a function of x and y, is equal to 0.

And we're done.