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x = 4sin(2y + 6)dx/dy = 4(2)cos(2y + 6)dx/dy = 8cos(2y + 6) ==> dy/dx = 1/8cos(2y + 6)sin²(2y + 6) + cos²(2y + 6) = 1cos(2y + 6) = √(1 - sin²(2y + 6))cos(2y + 6) = √(1 ...

first recognise ‘area under’ = integrationfunction is a product so by partsset x=u; exp(-x)=dv/dx integral(udv/dx)=uv-integral(vdu/dx)
du/dx =1; v=-exp(-x)ans=(x.-exp(-x))-integral(1.exp(-x)dx)ans=-x...

2 Secx = 2/CosxCotx = 1/Tan x = Cosx/SinxTherefore: 2SecCotx = 2/Cosx * Cosx/Sinx = 2/Sinx = 2Cosecx

work out in parts / ratio firstly work out how much one pencil costs, 50p divide by 5 = 10p1 pencil = 10p therefore, 2 pencils = 10p x 2 = 20p

Firstly, recognize that 2^3 is 8, so y must be close to 8.It will be helpful to then write y^3 as y^3= 8 + 0.08We can then factorize out 8.y^3=8(1+0.01)If we try and take the cube root of this expression....