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What is differentiation and how do I do it?

explain the following briefly: To work out the gradient, first principles, shortcutsexplain in detail: different methods

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How to integrate by parts

if f(x) = 7x-1 and g(x) = 4/(x-2), solve fg(x) = x

A curve has equation y = f(x) and passes through the point (4,22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7 use intergration to find f(x).

A curve is defined by the parametric equations x = 3 - 4t, and y = 1 + 2/t. Find dy/dx in terms of t.

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