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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...

*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...

Use the product rule:

d/dx(fg) = f'g + fg'

f = x²    f' = 2x   g = sin(x)  g' = cos(x)

answer = 2xsin(x) + x²cos(x)

As the tangent has the same gradient as the curve at the particular point, we need to find the gradient of the curve. To find the gradient we need to differentiate. Due to there being two variables in thi...