Find the Derivative - d/dz 1/(z^2+1)

Problem

d()/d(z)1/(z2+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 as (z2+1)(−1)

2. Apply the power rule by bringing the exponent −1 to the front and subtracting 1 from the exponent.

d(z2+1)/d(z)=−1*(z2+1)(−2)⋅d(z2+1)/d(z)

3. Apply the chain rule by finding the derivative of the inner function z2+1 with respect to z

d(z2+1)/d(z)=2*z

4. Multiply the results of the power rule and the chain rule together.

−1*(z2+1)(−2)⋅2*z=−2*z*(z2+1)(−2)

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

−2*z*(z2+1)(−2)=(−2*z)/((z2+1)2)

Final Answer

d()/d(z)1/(z2+1)=(−2*z)/((z2+1)2)

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