Find the Derivative - d/ds s/(1+s^2)

Problem

d()/d(s())s()/(1+s2())

Solution

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

2. Assign the numerator and denominator functions. Let u=s() and v=1+s2()

3. Differentiate the individual components.

d(s())/d(s())=1

d(1+s2)/d(s())=2*s()

4. Substitute these derivatives into the quotient rule formula.

d()/d(s())s()/(1+s2())=((1+s2)*(1)−(s)*(2*s))/((1+s2)2)

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

(1+s2−2*s2())/((1+s2)2)

1−s2()

Final Answer

d()/d(s())s()/(1+s2())=(1−s2())/((1+s2)2)

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