Find the Derivative - d/dx (4x)/(x^2+1)

Problem

d()/d(x)(4*x)/(x2+1)

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 numerator and denominator functions. Let u=4*x and v=x2+1

3. Differentiate the individual components. Find (d(4)*x)/d(x)=4 and d(x2+1)/d(x)=2*x

4. Substitute these values into the quotient rule formula.

d()/d(x)(4*x)/(x2+1)=((x2+1)*(4)−(4*x)*(2*x))/((x2+1)2)

5. Expand the terms in the numerator.

d()/d(x)(4*x)/(x2+1)=(4*x2+4−8*x2)/((x2+1)2)

6. Combine like terms to simplify the numerator.

d()/d(x)(4*x)/(x2+1)=(4−4*x2)/((x2+1)2)

Final Answer

d()/d(x)(4*x)/(x2+1)=(4−4*x2)/((x2+1)2)

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