Derivative of this is equal to the derivative of this.

So the derivative of the numerator is the derivative of 4x squared is 8x minus 5 over the derivative of the denominator is, well, derivative of 1 is 0.

Let's take the derivative of that, put it over the derivative of that.

Your derivative of the first term, derivative of x is 1 times the second term plus the derivative of the second term times the first term.

So the derivative of x is 1. times y to the negative 1 plus the derivative of y so

The derivative of this thing is going to be equal to the derivative of the first expression of the first function.

Then that equals the derivative of the first times the second function, plus the first function times the derivative of the second.

Well we learned this in the derivative module.

Well, derivative of x to the negative 1, we'll take the derivative of the first one times the second thing, and then the derivative of the second thing times the first thing.

This is the same thing as the derivative of f of x plus the derivative3 of g of x.

We take the derivative of the inside.

The derivative of a with respect to x is equal to the derivative of a with respect to b times the derivative of b with respect to x.

And the chain rule just tells us that the derivative of a with respect to c is equal to the derivative of a with respect to b times the derivative of b with respect to c.

It's the derivative of the first expression times the second expression plus the derivative of the second expression times the first.

I'm not using the definition of the derivative e, or the definition of the derivative of e to the x.

So the derivative of f.

What does it mean, derivative?

The derivative of e to the x.

Take the derivative of the first term and the derivative of the first term isn't a joke you take the derivative of the inside first, let's do the chain rule, derivative of the inside first.

So we can just say that the derivative of this is just 5 times the derivative of x squared.

So the derivative of this term we take the derivative of the inside, which is pretty easy.

The derivative of a with respect to x is equal to the derivative of a with respect to y times the derivative of y with respect to x, right?

And then when I take the derivative of the inside, I'm really taking the derivative of b with respect to c.

What's the derivative of the inside?

So we figured out the derivative of this so far, and then we want to figure out the derivative of this, so we'll add it, right, because we're trying to figure the derivative of this entire expression.

The derivative of x is 1, derivative of x squared is 2x and so on, right?

Derivative of negative 6x is negative 6.

So we want the derivative of this.

Well, it's the antiderivative.

Well, what's the derivative of t?

The derivative of t is 1.

And that's why they are called derivative instruments.

We take the derivative of the inside.

Find the derivative of both sides.

The derivative of 3x x plus 10.

So the derivative of the first term.

Plus the derivative of 5x is 5.

So what's the derivative of the first expression?

So what's the derivative of this?

So it's going to be equal to so the derivative of natural

So the chain rule just says that the derivative of f of x or f prime of x is equal to the derivative of this inner function, g prime of x times the derivative of this h function, h prime of x.

The derivative with this respect to x the derivative of the left side with respect to x is the same as the derivative of the right side with respect to x.

The derivative of a with respect to c is equal to this, which is this, 2b, the derivative of a with respect to b times the derivative of b with respect to c.

So dv the derivative of v with respect to t is equal to the derivative of v with respect to h.

And then we take the derivative of the outside function or the derivative of the outside function with respect to the inner function.