Calculating the Derivative of y=[(1-x)/X]^2

To calculate the derivative of y=[(1-x)/X]^2, we need to use the chain rule of differentiation. We can break it down into steps as follows:

Step 1: Rewrite the function using the quotient rule of differentiation.

y = (1-x)^2 / x^2

Step 2: Expand the numerator using the binomial theorem.

y = (1 - 2x + x^2) / x^2

Step 3: Simplify the numerator.

y = 1/x^2 - 2/x + 1

Step 4: Calculate the derivative of each term using the power rule of differentiation.

dy/dx = -2/x^2 + 2/x^3

Step 5: Simplify the expression.

dy/dx = 2(x-1) / x^3

Explanation:

The derivative of a function tells us the rate at which the function is changing at any given point. In this case, we are calculating the derivative of y with respect to x, which tells us how fast y is changing as x changes.

To calculate the derivative of y=[(1-x)/X]^2, we need to use the chain rule of differentiation. We first rewrite the function using the quotient rule of differentiation, then expand the numerator using the binomial theorem and simplify the numerator.

Next, we calculate the derivative of each term using the power rule of differentiation and simplify the expression to obtain our final answer.

The derivative of y=[(1-x)/X]^2 is 2(x-1) / x^3.