Differentials Consider the following functions and express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x)dx.


f(x) = ln (1 - x)

Verified step by step guidance

1. Identify the function f(x) = ln(1 - x) and determine its derivative f'(x) using the rules of differentiation.
2. Apply the chain rule to find f'(x), which involves differentiating the natural logarithm function.
3. Express the relationship between the small change in x (dx) and the corresponding change in y (dy) using the formula dy = f'(x)dx.
4. Substitute the expression for f'(x) into the equation dy = f'(x)dx to relate dy and dx explicitly.
5. Interpret the result to understand how a small change in x affects the change in y for the given function.