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

Problem

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

Solution

1. Identify the function as a reciprocal or a composition of functions, which can be solved using the power rule combined with the chain rule by rewriting the expression.

2. Rewrite the expression using a negative exponent to avoid the quotient rule.

1/(x2+1)=(x2+1)(−1)

3. Apply the chain rule, which states that the derivative of un is n*u(n−1)⋅d(u)/d(x)

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

4. Differentiate the inner function x2+1 using the power rule.

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

5. Substitute the inner derivative back into the expression.

−1*(x2+1)(−2)⋅2*x

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

(−2*x)/((x2+1)2)

Final Answer

d()/d(x)1/(x2+1)=−(2*x)/((x2+1)2)

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