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

Problem

d()/d(x)(x2)/(x+1)

Solution

1. Identify the rule needed for the derivative of a quotient, which is the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the numerator and denominator functions: u=x2 and v=x+1

3. Differentiate the individual components: d(x2)/d(x)=2*x and d(x+1)/d(x)=1

4. Substitute these into the quotient rule formula:

((x+1)*(2*x)−(x2)*(1))/((x+1)2)

5. Expand the terms in the numerator:

(2*x2+2*x−x2)/((x+1)2)

6. Combine like terms to simplify the numerator:

(x2+2*x)/((x+1)2)

Final Answer

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

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