Y Y Yes.

What's the anti derivative of y, the function y or y d y.

Y y yeah, right.

But then we have a y. y to the first. y squared. y to the third. y to the fourth. y to the fifth.

And then y times y, well that's just y squared,

Y and a y squared.

Here f of y is square root of y squared d y.

Delta y just means change in y.

Square root of y squared is y.

log of y is 1 over y.

Square root of y squared is y.

Change in y would be this y.

The y terms become 4 times y minus 2 squared. y minus 2 squared.

And then finally, y to the sixth over y to the fifth, that's y to the 6 minus 5 power, which is just y to the first power, or just y, so times y.

And then I have to worry about the y terms, times y squared times another y squared times another y squared.

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We could write y square roots of y.

Let's say y actually I'm tired of y.

So y plus y plus 1 plus 7.

So the derivative of natural log of y with respect to y is 1 y.

Or it's y to the first, times y to the first, which is also y squared.

Well, let's call that y general. y sub g.

And then finally, we have y divided by y.

It's gotta be YOU! You! ahem Y y you!

Plus 3 squared plus, now y, y is 2.

Let me draw some y values, positive y values.

line's y intercept is going to be f y.

Let's call this angle y and this angle y.

We have x y 180 x y 180 degrees

That's their y intercept. y is equal to 0.

Minus q of x2 of y and y dy.

Which makes sense, this is the middle term. y to the sixth. y to the seventh. y to the eighth. y to the ninth.

Let me graph y equals x. y equals x. y equals x is that line right there.

The upper y curve is x1 of y, so the upper y curve looks something like that.

It's the derivative of y with respect to y is 1, times the derivative of y with respect to x, which is just y prime.

So this is Y of s, and this Y of s, times Y of s, and then we have the non Y of s terms.