Find the Derivative - d/dx (3x)/(x^2+1)

Problem

d()/d(x)(3*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=3*x and v=x2+1

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

4. Substitute these values into the quotient rule formula:

((x2+1)*(3)−(3*x)*(2*x))/((x2+1)2)

5. Expand the terms in the numerator:

(3*x2+3−6*x2)/((x2+1)2)

6. Combine like terms to simplify the expression:

(3−3*x2)/((x2+1)2)

Final Answer

d()/d(x)(3*x)/(x2+1)=(3−3*x2)/((x2+1)2)

Want more problems? Check here!