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

Problem

d()/d(x)(−x+1)/(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, where u=−x+1 and v=x+1

3. Differentiate the numerator u to find d(u)/d(x)=−1

4. Differentiate the denominator v to find d(v)/d(x)=1

5. Substitute these values into the quotient rule formula (vd(u)/d(x)−ud(v)/d(x))/(v2)

((x+1)*(−1)−(−x+1)*(1))/((x+1)2)

6. Distribute the terms in the numerator.

(−x−1+x−1)/((x+1)2)

7. Simplify the numerator by combining like terms.

(−2)/((x+1)2)

Final Answer

d()/d(x)(−x+1)/(x+1)=−2/((x+1)2)

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