Find the Derivative - d/dx f(x)=1/(x-1)

Problem

d()/d(x)1/(x−1)

Solution

1. Identify the function as a reciprocal or a power by rewriting the expression using a negative exponent.

1/(x−1)=(x−1)(−1)

2. Apply the power rule and the chain rule, where the derivative of un is n*u(n−1)⋅d(u)/d(x)

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

3. Differentiate the inner function x−1 with respect to x

d(x−1)/d(x)=1

4. Simplify the expression by multiplying the terms and moving the negative exponent back to the denominator.

−1*(x−1)(−2)⋅1=−1/((x−1)2)

Final Answer

d()/d(x)1/(x−1)=−1/((x−1)2)

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