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

Problem

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

Solution

1. Identify the function as a reciprocal of a composite function, which can be rewritten using a negative exponent as (1+x2)(−1)

2. Apply the power rule and the chain rule by bringing the exponent to the front and subtracting one from the exponent.

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

3. Differentiate the inner function 1+x2 with respect to x

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

4. Substitute the derivative of the inner function back into the expression.

−1*(1+x2)(−2)⋅2*x

5. Simplify the expression by moving the term with the negative exponent to the denominator.

(−2*x)/((1+x2)2)

Final Answer

d()/d(x)1/(1+x2)=−(2*x)/((1+x2)2)

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