What is the derivative of y = x / (1 - x) ? Group of answer choices y' = 2x / (x - 1)² y' = -2x / (x - 1)² y' = 1 / (x - 1)² y' = -1 / (x - 1)²

To find the derivative of the function y = x / (1 - x), we can use the quotient rule. The quotient rule states that the derivative of a quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

Here, our numerator function (u) is x and our denominator function (v) is (1 - x).

The derivative of u (u') is 1 and the derivative of v (v') is -1.

Applying the quotient rule, we get:

y' = [v * u' - u * v'] / v² = [(1 - x) * 1 - x * -1] / (1 - x)² = [1 - x + x] / (1 - x)² = 1 / (1 - x)²

So, the derivative of y = x / (1 - x) is y' = 1 / (1 - x)².

Therefore, the correct answer is:

y' = 1 / (1 - x)²