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

Problem

d()/d(x)(x2+1)/(x2−1)

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 variables for the numerator and denominator. Let u=x2+1 and v=x2−1

3. Differentiate both u and v with respect to x

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

d(x2−1)/d(x)=2*x

4. Substitute these components into the quotient rule formula.

((x2−1)*(2*x)−(x2+1)*(2*x))/((x2−1)2)

5. Expand the terms in the numerator.

(2*x3−2*x−(2*x3+2*x))/((x2−1)2)

6. Simplify the numerator by combining like terms.

(2*x3−2*x−2*x3−2*x)/((x2−1)2)

(−4*x)/((x2−1)2)

Final Answer

d()/d(x)(x2+1)/(x2−1)=(−4*x)/((x2−1)2)

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