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a-level maths student here, differentiation is finding the gradient, so dy/dx (or sometimes written as f'(x) ) = change in y divided by change in x. Usually its used in finding points/co-ords on a curve, mostly stationary points (gradient is 0) i.e maxima and minima. You also use diffferentiation in modelling, so using it to find maximum/minimum volumes/lengths for a container when ur given the surface area for example.

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