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Firstly we must notice that we can differentiate each term separately.

Starting with the 2xy term, we must use the product rule as x and y are two variable that will differentiate. Setting u=2x and...

To see where the graph is greater than zero, we start by finding where it meets zero. By factorising (x^2 - 7x - 18), we find it equals (x-9)(x+2). The expression equals zero at the points x = 9 and x = -...

To solve this question, we need to use the chain rule, because the function is too complicated to solve simply by inspection. The chain rule says that dy/dx = dy/du × du/dx, where u is a function of x. In...

Straight away we notice that two trigonometric terms on the left hand side have 2x but there are no 2x on the right hand side therefore we realise that this question will require double angle formulae. If...

If you have an expression like 6x^2, to integrate it you have to add 1 to the power. Therefore, the new power will be 3. Then divide the whole expression by the new power so it will be 6x^3 divided by 3, ...