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

Problem

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

Solution

1. Identify the rule needed for the derivative of a quotient, which is the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the numerator and denominator functions: u=2*x and v=x2+1

3. Differentiate the individual components: (d(2)*x)/d(x)=2 and (d(x2)+1)/d(x)=2*x

4. Substitute these values into the quotient rule formula:

((x2+1)*(2)−(2*x)*(2*x))/((x2+1)2)

5. Expand the terms in the numerator:

(2*x2+2−4*x2)/((x2+1)2)

6. Combine like terms to simplify the expression:

(−2*x2+2)/((x2+1)2)

7. Factor out the common constant in the numerator:

(2*(1−x2))/((x2+1)2)

Final Answer

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

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