Theta one gets updated as theta one minus alpha times

d d theta one J of theta one, right?

And as an aside, this derivative term, right, if you're

wondering why I changed the notation from these partial derivative symbols.

If you don't know what the difference is between these partial derivative symbols

and the dd theta, don't worry about it.

Technically in mathematics you call this a partial derivative and

call this a derivative, depending on the number of parameters in the function J.

But that's a mathematical technicality.

And so for the purpose of this lecture,

think of these partial symbols and d, d theta 1, as exactly the same thing.

And don't worry about what the real difference is.

I'm gonna try to use the mathematically precise notation, but for

our purposes these two notations are really the same thing.

And so let's see what this equation will do.

So we're going to compute this derivative, not sure if you've seen derivatives in

calculus before, but what the derivative at this point does, is basically saying,

now let's take the tangent to that point, like that straight line, that red line,

is just touching this function, and let's look at the slope of this red line.

That's what the derivative is,

it's saying what's the slope of the line that is just tangent to the function.

Okay, the slope of a line is just this height divided by this horizontal thing.

Now, this line has a positive slope,

so it has a positive derivative.

And so my update to theta is going to be theta 1,

it gets updated as theta 1, minus alpha times some positive number.