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Note: sorry for the lump of text, the format of the site will not allow paragraphs unfortunately... when I put // it means new section or new paragraph, sorry again for the inconvenience caused.// Differenti...

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 multipl...

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 as ...

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. By u...