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But why, you may be asking yourself, would anyone ever want to take two derivatives of something? Because nature does—and it does it all the time. Or, rather, our models of nature do it all the time. For example, in Newton’s law of motion, F = ma, the acceleration a involves two derivatives. To see why, remember that the acceleration is the derivative of speed and speed is the derivative of distance. That makes acceleration the derivative of the derivative of distance, or to put it more concisely, the second derivative of distance. Second derivatives come up everywhere in physics and
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