First time I smiled doing a derivative.

First time I smiled doing a derivative.

First time I smiled doing a derivative.

Have I been saying derivative the whole time?

Times the derivative of y with respect to time.

So the derivative with respect to time of the volume.

The second derivative with respect to time is the acceleration.

So let's take the derivative with respect time on both sides.

Now let's take the derivative of this with respect to time.

So what's the derivative with respect to time of x squared?

So that's 2x times the derivative of x with respect to time.

So what is the derivative of our position vector with respect to time

And what's the derivative with respect to time of this side of the equation?

So let's take the derivative with respect to time of x squared plus y squared.

So, we get 4i plus... and then the derivative the second derivative, or the second derivative of y with respect to t is just the derivative of the first derivative.

So our second derivative is the derivative of this.

Well, the highest derivative here is the second derivative.

So we just have to take the derivative of the bacteria function with respect to time.

1st derivative

2nd derivative

The Derivative.

Derivative of this is equal to the derivative of this.

You could take the derivative, and the derivative is continuous.

And this, of course, is just going to be equal to the derivative of x of the derivative of x the second derivative of x(t) is just the derivative of the first derivative.

Well, the second derivative is just the slope of the derivative.

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.

Show first derivative

Show 1st derivative

Show second derivative

Show 2nd derivative

Derivative chain rule.

Derivative equals 0.

That's the derivative.

The second derivative.

Or the derivative.

1st derivative r.

This is the anti derivative and this is also the anti derivative.

And someone wrote just on YouTube it was a YouTube comment First time I smiled doing a derivative.

Or another way you could view it is what is the derivative at time is equal to 3?

Take the derivative operator because we're taking the derivative with respect to x.

Well, you could view it as the derivative of the first derivative, right?

I'll write the derivative operator, the derivative oh y with respect to x.

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

Or the second derivative.

What's the second derivative?