Question

Let f(x) = ln(1 - 2x). Which of the following represents f '(x) for all values of x for which the function is defined?

1) 2/(1-2x)
2) -2/(1-2x)
3) 2/(1+2x)
4) -2/(1+2x)

Answer 1

The derivative of the given function f(x) = ln(1 - 2x) is -2/(1 - 2x).

Step-by-step explanation:

The function f(x) is given as f(x) = ln(1 - 2x).

To find the derivative of f(x), we need to apply the chain rule. The derivative of ln(u) is 1/u multiplied by the derivative of u, where u is the argument of the natural logarithm.

Using the chain rule, the derivative f'(x) is equal to:

f'(x) = 1/(1 - 2x) * (-2)

Simplifying further, we get:

f'(x) = -2/(1 - 2x)

Therefore, the correct answer is option 2: -2/(1 - 2x).