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Bring the power down and multiply it to the value directly before x, and then remove 1 from the power after this. So in this instance 12 has no x or power with it, therefore it disappears because you mult...

First, you add the 5+3 to get 8. Now you know there are 8 'portions' of the £80 needed to be shared out. So £80/8 is 10. Sam needs 5 portions so 5x10=50 and Jack needs 3 portions so 3x£10 is £30.

This would be on a non-calculator paper and so it wants an answer in the form 2^n as without a calculator it is too difficult to work out. You can only do this multiplication if you change the 8 into 2^3 ...

Here you need to use the formula that the differential of e^f(x), where f(x) is any function, is equal to f'(x)e^f(x). So for our function we differentiate xsinx using product rule to give sinx + xcosx. ...

This question requires you to use the trigonometric identity sin(A+B)=sinAcosB + sinBcosA. The difficulty in this problem is noticing that you need to substitute 2A for A+A and then you can simply put thi...