Find the Derivative - d/dx y=(x^2-6x+12)/(x-4)

Problem

d()/d(x)(x2−6*x+12)/(x−4)

Solution

1. Identify the function as a quotient of two polynomials, u=x2−6*x+12 and v=x−4

2. Apply the quotient rule formula, which states that d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

3. Differentiate the numerator u to find d(u)/d(x)=2*x−6

4. Differentiate the denominator v to find d(v)/d(x)=1

5. Substitute these derivatives into the quotient rule formula.

d()/d(x)(x2−6*x+12)/(x−4)=((x−4)*(2*x−6)−(x2−6*x+12)*(1))/((x−4)2)

6. Expand the terms in the numerator.

(x−4)*(2*x−6)=2*x2−6*x−8*x+24=2*x2−14*x+24

7. Subtract the second part of the numerator.

(2*x2−14*x+24)−(x2−6*x+12)=2*x2−14*x+24−x2+6*x−12

8. Combine like terms to simplify the numerator.

x2−8*x+12

9. Factor the numerator if possible to see if any terms cancel.

x2−8*x+12=(x−2)*(x−6)

Final Answer

d()/d(x)(x2−6*x+12)/(x−4)=(x2−8*x+12)/((x−4)2)

Want more problems? Check here!