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

Problem

d()/d(x)(x2)/(x2+3)

Solution

1. Identify the rule needed for the derivative of a quotient of two functions, which is the quotient rule.

2. Apply the formula for the quotient rule, d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2) where u=x2 and v=x2+3

3. Differentiate the numerator and denominator separately to find d(x2)/d(x)=2*x and d(x2+3)/d(x)=2*x

4. Substitute these derivatives into the quotient rule formula.

((x2+3)*(2*x)−(x2)*(2*x))/((x2+3)2)

5. Expand the terms in the numerator to prepare for simplification.

(2*x3+6*x−2*x3)/((x2+3)2)

6. Simplify the numerator by combining like terms, noting that 2*x3−2*x3=0

(6*x)/((x2+3)2)

Final Answer

d()/d(x)(x2)/(x2+3)=(6*x)/((x2+3)2)

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