Search over 10,000 free study notes

The first step would be to consider each of the powers individually, work out their value and then proceed with the subtraction to end up with a result. Firstly, as this question is to be done without a c...

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. ...