To find dy/dx, we need to differentiate y with respect to x.
We can start by using the chain rule, which states that if we have a function of the form f(g(x)), the derivative of that function with respect to x is f'(g(x)) * g'(x).
In this case, we have y = 243(4x + 5)-2, which can be written as y = 243/(4x + 5)^2.
Using the chain rule, we have:
dy/dx = d/dx(243/(4x + 5)^2)
= -2 * 243 / (4x + 5)^3 * d/dx(4x + 5)
= -2 * 243 / (4x + 5)^3 * 4
= -1944 / (4x + 5)^3
Now, to find the value of dy/dx when x = 1, we just need to substitute x = 1 into the expression we found above:
dy/dx = -1944 / (4(1) + 5)^3
= -1944 / 729
= -8/3
Therefore, the answer is option A: -83.
To summarize, we used the chain rule to differentiate y with respect to x, which gave us an expression for dy/dx in terms of x. We then substituted x = 1 to find the value of dy/dx at that point.