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At the minimum point, the gradient will be zero, so we differentiate the equation, giving us dy/dx = 3e^3x - 12e^2x. If the gradient is zero at the minimum point, we can set dy/dx = 0,...

First split up the fraction into partial fractions as this is more easily integrated. It can be seen that the denominator has factors y and (3y+2), therefore we can say the original fraction is equal to p...

Firstly we integrate x^2 with respect to x which is (x^3)/3 as we integrate polynomials by adding a power then dividing by that power, (x^n+1)/n+1.Then we multiply by the 5 we have from earlier which give...

Split into partial fractions: (3x +2) / (x² - 5x +6) = A / (x-3) + B / (x-2) => 3x + 2 = A(x-2) + B(x-3) let x =...

Use product rule i.e. (uv)'=u'v+uv'Set u=e^x and differentiate to find u'=e^x Set v=cosx and differentiate to find v'=-sinxTherefore (uv)' where uv=e^xcosx =e^xcosx + e^x(-sinx)=e^xcosx - e^xsinx=e^x(cosx...