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

Problem

d(ln(1−x))/d(x)

Solution

1. Identify the outer function as ln(u) and the inner function as u=1−x

2. Apply the chain rule, which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x)

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

4. Substitute the inner function and its derivative back into the chain rule formula.

5. Simplify the resulting expression by multiplying the terms.

Final Answer

d(ln(1−x))/d(x)=1/(x−1)

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