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We can write the two numbers as x and 1000-x, because x+(1000-x) = 1000 for any x we pick. Now we want to maximise the product x(1000-x); expanding the brackets gives us 1000x-x² which is easie...

Using the chain rule we differentiate the ‘outside function’, then differentiate the ‘inside function’ and multiply both derivatives together giving 2sin(x)cos(x)

De Moivre's theorem states that e^ix= cos(x) + isin(x) or that e^i5x= cos(5x)+ isin(5x). If the real components of both sides of this equation is taken we can see that : cos(5x) = Re[e...

This is an actual question from an EdExcel C3 paper worth 4 marks. Ok so first thing we do is look at the function and try and determine which of our 3 differentiation rules we use. Is it a Product / Quot...