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

Problem

d()/d(x)1/(2*x−3)

Solution

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

1/(2*x−3)=(2*x−3)(−1)

2. Apply the chain rule by differentiating the outer function with respect to the inner function and then multiplying by the derivative of the inner function.

d(2*x−3)/d(x)=−1*(2*x−3)(−2)⋅d(2*x−3)/d(x)

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

d(2*x−3)/d(x)=2

4. Substitute the derivative of the inner function back into the expression.

−1*(2*x−3)(−2)⋅2=−2*(2*x−3)(−2)

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

−2*(2*x−3)(−2)=(−2)/((2*x−3)2)

Final Answer

d()/d(x)1/(2*x−3)=−2/((2*x−3)2)

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