Question

Find the derivative of the function. F(t) = e^(3t sin(2t))

Answer 1

To find the derivative of the given function F(t) = e^(3t sin(2t)), use the chain rule to find the derivative of the entire function.

Step-by-step explanation:

To find the derivative of the given function F(t) = e^(3t sin(2t)), we can use the chain rule.

1. Start by finding the derivative of the exponent, which is e^(3t sin(2t)).
2. Next, find the derivative of the outer function with respect to the inner function.
3. Finally, multiply the two derivatives together to find the derivative of the entire function.

Using this process, the derivative of F(t) = e^(3t sin(2t)) is:

F'(t) = e^(3t sin(2t)) * (3*cos(2t) + 6t*cos(2t))