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

Problem

d()/d(x)x/(x+2)

Solution

1. Identify the rule needed for differentiation. Since the expression is a quotient of two functions, u=x and v=x+2 use the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Differentiate the numerator and the denominator separately.

d(x)/d(x)=1

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

3. Apply the quotient rule by substituting the functions and their derivatives into the formula.

((x+2)*(1)−(x)*(1))/((x+2)2)

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

(x+2−x)/((x+2)2)

2/((x+2)2)

Final Answer

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

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