Find the Derivative - d/d@VAR f(x)=x/(x+1)

Problem

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

Solution

1. Identify the rule needed for the derivative of a quotient of two functions, which is the quotient rule.

2. Apply the formula for the quotient rule, d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2) where u=x and v=x+1

3. Differentiate the numerator and denominator separately to find d(x)/d(x)=1 and 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)

6. Finalize the expression by reducing the numerator:

1/((x+1)2)

Final Answer

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

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