Find the Derivative - d/dx natural log of x-1

Problem

d(ln(x−1))/d(x)

Solution

1. Identify the function as a composition of the natural logarithm and a linear function, which requires the use of the Chain Rule.

2. Apply the formula for the derivative of ln(u) which is 1/u⋅d(u)/d(x)

3. Substitute u=x−1 into the derivative formula.

4. Differentiate the inner function x−1 with respect to x which results in 1

5. Simplify the expression by multiplying the terms.

Final Answer

d(ln(x−1))/d(x)=1/(x−1)

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