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Differentiate the first term 2x3 as normal by multiplying the coefficient of x by the power and subtracting the power by 1 to get 6x² . For the next term you have to use the product rule as you...

4x/(x²-9)-2/(x+3) = 4x/((x+3)(x-3))-2/(x+3) = 4x/((x+3)(x-3))-2(x-3)/((x+3)(x-3)) = (4x-2(x-3))/((x+3)(x-3)) = (2x+6)/((x+3)(x-3) = (2(x+3))/((x+3)(x-3)) = 2/(x-3)

For x = 2, y = 16. Calculate the gradient of the curve at y = 2, dy/dx = 6x^2, dy/dx = 24. This is also the gradient of the tangent to the curve at x = 2. It is a rule that the products of the gradients o...

This question challenges a students skills with integration and trigonometry a very common question on Core 4 papers that can leave students struggling. First we use our knowledge that cosecy=1/siny and m...