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Differentiate by multiply by the power and then minus 1 from the power. Use the rule: y= ax^b -> dy/dx = abx^(b-1)

dy/dx = 3 x 2x^(3-1) + -1 x 2x^(-1-1) + 0 dy/dx = 6x^2 - 2x^-2

Using indices rules: y^a x y^b = y^(a+b), y^a / y^b = y^(a-b) Simplifying the numerator: b^6 x b^2 = b^(6+2) = b^8 Simplifying the whole fraction: b^8 / b^4 = b^(8-4) = b^4 Fully simplified answer is b^...

Shop A-> Total Price = 30 plants x £2.49 =£74.70 Shop B-> VAT = 20% = 0.2 VAT = 0.2 x £58 = £11.60 Total Price = £11.60 + £58 = £69.60 OR

Total price = 1.2 x £58 = £69.60

Therefore Jes...

Use the method of integration by parts. uv-integral(v.du/dx). Make u equal to ln(x) and dv/dx equal to 1. Therefore v=x and du/dx=1/x. Hence uv=xln(x). And v.du/dx=x/x=1. Substituting these into the 'by p...

Firstly work out (using the sin cos tan triangle and soh cah toa) what cos 30° and tan 60° are equal to so tan 60° = √3 and cos 30° = √3 / 2 then substitute these values into the euqation giving 12 x √3 /...