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 fraction 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 to variables. Let u=x2−1 and v=x2+1

3. Differentiate both parts with respect to x

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

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

4. Substitute these values into the quotient rule formula.

((x2+1)*(2*x)−(x2−1)*(2*x))/((x2+1)2)

5. Distribute 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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