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i) There first step is to acknowledge the need for both product rule (d(uv)/dx=v.du/dx+u.dv/dx) and chain rule (dz/dx=dz/dy*dy/dx). Here, u=x^3 and v=ln(2x). Therefore, du/dx=3x^2 which is a standard diff...

Factorise means we want to turn x²-8x+15=0 into the form (x+a)(x+b)=0. We need to find the two whole numbers 'a' and 'b' which equal -8 (from the -8x part) when added together,...

For a quotient f(x) = u(x)/v(x), the derivative is f'(x) = (vu'(x) - uv'(x))/v(x)². Applying this to the given function, we find u(x) = x+3 and v(x) = 2x-5. So, u'(x) = 1 and v'(x) = 2...

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. We can work this out for the sequence 11, 17, 23, 29. ...