What is differentiation and why is it useful?

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Although differentiation is often taught in an abstract way, it's applications are virtually limitless. It's primary purpose is to determine the gradient of a line at a given point on a curve. Unlike with the gradient of a straight line, which is constant at all points on the line, the gradient of a curve is different at every point. Differentiation is therefore the method used to find the gradient at a given point. 

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