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

Problem

d()/d(x)x/(x+y)

Solution

1. Identify the rule needed for differentiation. Since the expression is a fraction where the numerator and denominator both contain the variable x use the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the variables for the quotient rule. Let u=x and v=x+y

3. Differentiate the numerator and denominator with respect to x Note that y is treated as a constant in this context.

d(x)/d(x)=1

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

4. Apply the quotient rule formula by substituting the derivatives.

((x+y)*(1)−x(1))/((x+y)2)

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

(x+y−x)/((x+y)2)

y/((x+y)2)

Final Answer

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

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