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The general rule for differentiation is multiply by the power and decrease the power by one.
So if we take each term individually starting with 5x^2, and multiply by the power giving 10 then reduce t...

There are 2 methods of solving this: completing the square or calculus, which makes this a versatile question for both GCSE and A Level students. It is also fairly simple to adapt.
Using calculus, th...

First rearrange x - 2y = -3 by adding 2y to each side to give x = -3 + 2ySubstitute this into the first eq. to give 3(-3 +2y) + y = 19Expand brackets first: -9 + 6y + y = 19Rearrange and simplify by colle...

dy/dx = 4/(x^2+5) - 4x(2x)/(x^2+5)dy/dx= 4(5-x^2)/(x^2+5)^2Part B4(5-x^2)/(x^2+5)^2<05-x^2<05<x^2

First we need to use the factor theorem to find a factor.f(1)=-25 so x-1 is not a factorf(-1)=9 so x+1 is not a factorf(2)=0 so x-2 is a factorSo x-2 is our starting point, we need to polynomial division ...