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

Problem

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

Solution

1. Identify the rule needed for differentiation. Since the expression is a quotient of two functions, u=x and v=x+1 use the quotient rule.

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

3. Calculate the derivatives of the numerator and the denominator.

d(x)/d(x)=1

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

4. Substitute these values into the quotient rule formula.

((x+1)*(1)−(x)*(1))/((x+1)2)

5. Simplify the numerator by distributing and combining like terms.

(x+1−x)/((x+1)2)

1/((x+1)2)

Final Answer

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

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