Find the Derivative - d/dx (x+3)/(x-1)

Problem

d()/d(x)(x+3)/(x−1)

Solution

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

2. Assign the numerator and denominator functions. Let u=x+3 and v=x−1

3. Differentiate the individual parts. The derivative of the numerator is d(x+3)/d(x)=1 and the derivative of the denominator is d(x−1)/d(x)=1

4. Substitute these values into the quotient rule formula.

d()/d(x)(x+3)/(x−1)=((x−1)*(1)−(x+3)*(1))/((x−1)2)

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

(x−1−x−3)/((x−1)2)

6. Combine the constants in the numerator to reach the final simplified form.

(−4)/((x−1)2)

Final Answer

d()/d(x)(x+3)/(x−1)=−4/((x−1)2)

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