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A derivative is a mathematical description of how one quantity will change with respect to another. For example the 1st derivative of some function will give you the gradient of the tangent at every point...

Partial fractions are just another technique to simplify expressions to make them easier to manipulate in more complex questions. This is a low mark questions, testing your skills at using partial frac...

First you need to find the vector AB. This is equal to -OA+OB.

OA and OB are equal to the position vectors of A and B respectively so

 -OA+OB=  -2i - 6j + k + 3i + 4j + k = ...

This type of equation involves a modulus, this the component enclosed in the straight lines, |2x+1|.

A modulus takes the absolute value of its contents, this means that regardless of the input...

As the expression contains 4 separate terms that are added together, we can treat this as 4 separate differentiations. The general rule for differentiation for a general term bx^n is (bn)x^(n-1...