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Suppose a cubic crystal is growing so that the side changes at the rate of 10mm per second when the side length is 20 mm. If I want to know how fast the volume of the cube is growing at that time, I must use the equation V=x^3 and take the implicit derivative with respect to t and solve for dV/dt. or Suppose a plane is headed on a course of 050 at 300 mph and another is headed due north at 500 mph. If you want to know how fast the direct distance between them is changing, you must use implicit differentiation. In short, for everyday going to the grocery store type activities you won't need implicit differentiation. For complicated problems involving different rates of change you need to use implicit differentiation.
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