Find the Derivative - d/dx 5/(x^2+1)

Problem

d()/d(x)5/(x2+1)

Solution

1. Identify the expression as a constant divided by a function, which can be rewritten using a negative exponent to apply the power rule and chain rule.

5/(x2+1)=5*(x2+1)(−1)

2. Apply the power rule by bringing the exponent down and subtracting one from the exponent.

d()/d(x)*5*(x2+1)(−1)=−5*(x2+1)(−2)⋅d(x2+1)/d(x)

3. Apply the chain rule by finding the derivative of the inner function x2+1

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

4. Multiply the results together to find the derivative.

−5*(x2+1)(−2)⋅2*x=−10*x*(x2+1)(−2)

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

(−10*x)/((x2+1)2)

Final Answer

d()/d(x)5/(x2+1)=−(10*x)/((x2+1)2)

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