What does differentiation actually do?

Differentiation allows you to find the rate of change of a variable relative to another, which is basically the gradient. So if you had a speed-time graph, finding the amount that speed changes over a given time will get you acceleration.

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Simplify the following algebraic fraction; (3x^2 - x - 2) / ((1/2)x + (1/3)).


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integrate 1+ln(x) with respect to x


Given that y = (( 4x + 1 )^3)sin(2x), find dy/dx.