Find the Derivative - d/dx x/(x^2-1)

Problem

d()/d(x)x/(x2−1)

Solution

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

2. Assign the variables for the numerator and denominator. Let u=x and v=x2−1

3. Differentiate the individual components.

d(u)/d(x)=1

d(v)/d(x)=2*x

4. Substitute these values into the quotient rule formula.

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

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

(x2−1−2*x2)/((x2−1)2)

−x2−1=−(x2+1)

Final Answer

d()/d(x)x/(x2−1)=−(x2+1)/((x2−1)2)

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