Find the Derivative - d/dx 1/(x^2+3x-1)

Problem

d()/d(x)1/(x2+3*x−1)

Solution

1. Identify the function as a reciprocal of a polynomial, which can be written as a power with a negative exponent: (x2+3*x−1)(−1)

2. Apply the chain rule by taking the derivative of the outer function (the power) and multiplying it by the derivative of the inner function (x2+3*x−1.

3. Differentiate the inner function using the power rule to get 2*x+3

4. Combine the results to form the derivative expression.

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

Final Answer

d()/d(x)1/(x2+3*x−1)=−(2*x+3)/((x2+3*x−1)2)

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