From the course: Assembling Calculus

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Acceleration: Higher derivatives

Acceleration: Higher derivatives

From the course: Assembling Calculus

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Acceleration: Higher derivatives

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- [Instructor] We've seen that derivative measures how a curve is changing. But the derivative is itself a curve, and that means it too has a derivative. This is called the second derivative. For example, if we take our X squared curve, we've seen that its derivative is a straight line with a slope of two. What's the second derivative? It would just be a constant equal to two everywhere. We should remember, we're always thinking about derivative with respect to something. For example, we're talking here about derivatives with respect to distance along the X axis. Second derivatives with respect to time are sometimes called acceleration. They're written as shown on the right hand side of the slide. On the left side, we've broken out our derivatives to show you've applied taking a derivative twice of our function of time. We would read this as a second derivative of F of T with respect to T. We think of these…

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