Search over 10,000 free study notes

This is an example of the chain rule.

The chain rule is the following: if y = uv, then dy/dx = udv/dx + vdu/dx

So in this case, u = ( 4x + 1)^3, v = sin(2x)

du/dx = (3)(4)( 4x + 1 )^2...

 ∫x² ln(4x)dx

Firstly , identify this question as integration by parts. Therefore set one half as value 'u' and one as value 'dv'.

Here we will set u = ln(4x).

Therefore: d...

There are two methods for solving simultaneous equations, the algebraic method or graphic method. While using graphs is a useful visual way to solve simultaneous equations, this is more time consuming and...

*The usual mistake with inequalities is not with a students algebra, but with lack of consideration of the inequality signs. During a tutorial I would show their false method and my correct one and also s...

1. x² + 15 x + 50 = 0 (rearrange by adding 50 to both sides)

2. (x + 10)(x + 5) = 0 (factorise the quadratic equation)

3. x + 10 = 0 or x + 5 = 0 (for the a...