Find the Derivative - d/dx -x+8/x+1

Problem

d()/d(x)(−x+8)/(x+1)

Solution

1. Identify the function as a quotient of two terms, u=−x+8 and v=x+1 which requires 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. Differentiate the numerator u=−x+8 to get d(u)/d(x)=−1

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

5. Substitute these derivatives into the quotient rule formula.

((x+1)*(−1)−(−x+8)*(1))/((x+1)2)

6. Distribute the terms in the numerator.

(−x−1+x−8)/((x+1)2)

7. Simplify the numerator by combining like terms.

(−9)/((x+1)2)

Final Answer

d()/d(x)(−x+8)/(x+1)=−9/((x+1)2)

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