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That technique for calculating derivatives only works for polynomial terms, that is terms of the form x^n, where n is some number. Here though our variable x is in the exponent, and so th...

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)