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

Problem

d()/d(x)x/(x^2+3)

Solution

1. Identify the rule needed for differentiation. Since the expression is a quotient of two functions, use the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v^2)

2. Assign the numerator and denominator functions. Let u=x and v=x^2+3

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

4. Substitute these values into the quotient rule formula.

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

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

(x^2+3−2*x^2)/((x^2+3)^2)

6. Combine the x^2 terms to reach the final simplified form.

(3−x^2)/((x^2+3)^2)

Final Answer

d()/d(x)x/(x^2+3)=(3−x^2)/((x^2+3)^2)

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