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

Problem

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

Solution

1. Rewrite the expression using a negative exponent to prepare for the power rule.

1/(2*x+1)=(2*x+1)(−1)

2. Apply the power rule and the chain rule by bringing the exponent to the front and subtracting one from the exponent, then multiplying by the derivative of the inner function.

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

3. Differentiate the inner function 2*x+1 with respect to x

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

4. Substitute the inner derivative back into the expression and simplify.

−1*(2*x+1)(−2)⋅2=−2*(2*x+1)(−2)

5. Rewrite the result using a positive exponent in the denominator.

−2*(2*x+1)(−2)=(−2)/((2*x+1)2)

Final Answer

d()/d(x)1/(2*x+1)=−2/((2*x+1)2)

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