Find the Derivative - d/d@VAR f(x)=x/(x^2-1)

Problem

d()/d(x)x/(x2−1)

Solution

1. Identify the rule needed for differentiation. Since the function is a quotient of two expressions, u=x and v=x2−1 use 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 to get d(x)/d(x)=1

4. Differentiate the denominator v=x2−1 to get d(x2−1)/d(x)=2*x

5. Substitute these derivatives into the quotient rule formula.

d()/d(x)x/(x2−1)=((x2−1)*(1)−(x)*(2*x))/((x2−1)2)

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

(x2−1−2*x2)/((x2−1)2)

(−x2−1)/((x2−1)2)

7. Factor out a negative sign from the numerator for the final form.

(−(x2+1))/((x2−1)2)

Final Answer

d()/d(x)x/(x2−1)=−(x2+1)/((x2−1)2)

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