Find the Derivative - d/dx (2x)/(x^2+100)

Problem

d()/d(x)(2*x)/(x2+100)

Solution

1. Identify the rule needed for differentiation. Since the expression is a quotient of two functions, apply the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the variables for the numerator and denominator. Let u=2*x and v=x2+100

3. Differentiate the individual components. Find (d(2)*x)/d(x)=2 and d(x2+100)/d(x)=2*x

4. Substitute these values into the quotient rule formula.

d()/d(x)(2*x)/(x2+100)=((x2+100)*(2)−(2*x)*(2*x))/((x2+100)2)

5. Simplify the numerator by distributing the 2 and multiplying the terms.

(2*x2+200−4*x2)/((x2+100)2)

6. Combine like terms in the numerator to reach the final simplified form.

(200−2*x2)/((x2+100)2)

Final Answer

d()/d(x)(2*x)/(x2+100)=(200−2*x2)/((x2+100)2)

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