Find the Derivative - d/dx (x^2-2x)/(x+1)

Problem

d()/d(x)(x2−2*x)/(x+1)

Solution

1. Identify the rule needed for the derivative. Since the expression is a fraction of two functions, use the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the numerator and denominator functions. Let u=x2−2*x and v=x+1

3. Differentiate the individual components.

d(x2−2*x)/d(x)=2*x−2

d(x+1)/d(x)=1

4. Substitute these values into the quotient rule formula.

((x+1)*(2*x−2)−(x2−2*x)*(1))/((x+1)2)

5. Expand the terms in the numerator.

(x+1)*(2*x−2)=2*x2−2*x+2*x−2=2*x2−2

(x2−2*x)*(1)=x2−2*x

6. Combine and simplify the numerator.

(2*x2−2)−(x2−2*x)=2*x2−2−x2+2*x

x2+2*x−2

Final Answer

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

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