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

Problem

d()/d(x)(x2)/(x2+1)

Solution

1. Identify the rule needed for differentiation. Since the function is a fraction of two differentiable functions, use 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=x2 and v=x2+1

3. Differentiate the individual components.

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

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

4. Substitute these into the quotient rule formula.

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

5. Expand the terms in the numerator.

(2*x3+2*x−2*x3)/((x2+1)2)

6. Simplify the numerator by combining like terms.

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

Final Answer

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

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