Final answer:
To find the derivative of the given function, we can use the product rule. The derivative of F(t) is 4(3t-1)^3 * 3 * (2t+1)^-3 + (3t-1)^4 * -3(2t+1)^-4 * 2.
Step-by-step explanation:
To find the derivative of the function F(t) = (3t-1)^4(2t+1)^-3, we can use the product rule. The product rule states that if we have two functions u(t) and v(t), the derivative of their product is given by u'(t)v(t) + u(t)v'(t).
In this case, u(t) = (3t-1)^4 and v(t) = (2t+1)^-3. Taking the derivative of u(t), we get u'(t) = 4(3t-1)^3 * 3 and taking the derivative of v(t), we get v'(t) = -3(2t+1)^-4 * 2. Plugging these values into the product rule formula, we get:
F'(t) = u'(t)v(t) + u(t)v'(t) = 4(3t-1)^3 * 3 * (2t+1)^-3 + (3t-1)^4 * -3(2t+1)^-4 * 2.
Simplifying this expression gives us the derivative of the function F(t).