Given that y={(x^2+4)(x−3)}/2x, find dy/dx in its simplest form.

Looking at the problem to start we can see that this is an algebraic division problemThere are three common methods you will come across for finding dy/dx for algebraic problems: The Chain Rule, The Product Rule and The Quotient Rule.This case will be solved using the Quotient Rule The Quotient Rule Formula is as follows: dy/dx= [v.(du/dx) + u(dv/dx)] / v^2Solving the Problem:Looking at the top half of the equation: simplifying to x^3 - 3x^2 +4x -12The bottom half of the equation remains the same simplified: 2xu= x^3 - 3x^2 +4x -12, du/dx= 3x^2-3x+4v= 2x dv/dx= 2dy/dx= [((2x)(3x^2-3x+4))+((x^3-3x^2 +4x -12) (2))] / (2x)(2x)Simplifying: dy/dx= 2x^3-3x^2+12/ 2x^2