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

Problem

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

Solution

1. Identify the rule needed for the derivative. Since the function is a quotient of two expressions, u=x and v=x2+1 use the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Differentiate the numerator and the denominator separately.

d(x)/d(x)=1

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

3. Apply the quotient rule formula by substituting the functions and their derivatives.

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

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

(x2+1−2*x2)/((x2+1)2)

1−x2

Final Answer

d()/d(x)x/(x2+1)=(1−x2)/((x2+1)2)

Want more problems? Check here!