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In differentiation you multiply the coefficient of the subject (what the value is multiplied by e.g. 3 is the coefficient of 3x⁶) by its exponent (the power that the value is raised to e.g. ...

This question is really straight forward

By using the Chain rule: f'(x) = uv' + u'v.

let u=3x, so u'=3

let v=(2x-1)^2, so v'=2x2(2x-1)=8x-4

Now, ...

You must be careful with these sorts of questions as although 1/(5-2x) is equivalent to (5-2x)^-1, when you integrate you would add one to the power and divide by the new power. But if you were to add one...

First we state the formula for sin(x+y)

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

Letting y = 2x

sin(x+2x) = sin(x)cos(2x) + cos(x)sin(2x)

Now sin(2...