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Since the quadratic has roots a and b, this means it can be fatored as 2(x-a)(x-b)=0. Expanding this out we get 2x^2-2(a+b)x+2ab=0 and matching the coefficients for the terms x^1 and x^0 we get a+b=-4 and...

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...