Final answer:
To find the derivative of the function y=((3)/(3x+1))^(4), use the chain rule and simplify the expression.
Step-by-step explanation:
To find the derivative of the function y=((3)/(3x+1))^(4), we can use the chain rule. The chain rule states that if we have a function f(g(x)), then the derivative of f(g(x)) is f'(g(x)) * g'(x). In this case, let f(u) = u^4 and g(x) = (3)/(3x+1). The derivative of f(u) is f'(u) = 4u^3 and the derivative of g(x) is g'(x) = -9/(3x+1)^2. Applying the chain rule, the derivative of y=((3)/(3x+1))^(4) is y' = f'(g(x)) * g'(x) = 4((3)/(3x+1))^3 * (-9/(3x+1)^2).