Answer:
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Explanation:
To differentiate y = 2 - 3x/(3 - 4x)^2, we can use the quotient rule for differentiation.
The quotient rule states that if f(x) = g(x)/h(x), then the derivative of f(x) is given by:
f'(x) = (g'(x)h(x) - g(x)h'(x)) / h(x)^2
In this case, we can set f(x) = 2 - 3x/(3 - 4x)^2, g(x) = 2, and h(x) = (3 - 4x)^2.
Substituting these values into the formula for the derivative of a quotient, we get:
f'(x) = (2*(3 - 4x)^2 - (2 - 3x)*(-8x)) / (3 - 4x)^4
Simplifying this expression gives:
f'(x) = (-24x^2 + 24x + 6) / (3 - 4x)^3
This is the derivative of y = 2 - 3x/(3 - 4x)^2.