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Unformatted text preview: 1 Some Simple Algorithms 1 for Calculating Derivatives The Derivative of a Constant is Zero Suppose we are told that o x x = where x o is a constant and x represents the position of an object on a straight line path, in other words, the distance that the object is in front of a start line. The derivative of x with respect to t x dt d dt dx written be also can which is then just the derivative of x o with respect to t . dt dx dt dx o = Now according to the mathematicians, the derivative of a constant is zero, so we have: = dt dx Does this make sense? This whole discussion about derivatives is relevant to the study of motion because the velocity of an object is the derivative of its position with respect to time: dt dx = v So what we are saying now is that if x = x o (where x o is a constant) then v = 0. Well x = x o means that the position of the object is not changing. So if we are talking about a car, for instance, then we must be talking about a parked car, and YES it does make sense for = dt dx , that is for v = 0, because the velocity of a parked car is indeed zero. 1 An algorithm is a sequence of steps. When you learned how to do long division, you were learning to execute an algorithm. The term is usually used in computer science where the goal is often to write an algorithm in a language that a computer can understand. But the term is not limited to computer science. In fact, you have been executing algorithms yourself ever since you first learned that one plus one is two. 2 The Derivative of t With Respect to t Is 1....
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- Winter '12
- Derivative, dt, constant times