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What is differentiation and why is it useful?

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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