40 POINTS Find the derivative with respect to x of the integral from 2 to x squared of the cosine of the quantity t squared plus 1, dt.

(see picture attached)

Answer choices:
– 2xsin(x^4 + 1)
2xcos(x^4 + 1)
– 4x^3 sin(x^4 + 1)
4x^3 cos(x^4 + 1)

A. the following events are mutually exclusive: living in california and watching american idol. true or false b. the number of patients seen by an outpatient practice is an example of a discrete random variable. true or false c. the law of large numbers states that as the number of times an event experiment is conducted increases, the likelihood of the actual probability of an event approaching the theoretical probability decreases. true or false d. measuring the time it takes for patients to enter the operating room is an example of a continuous random variable. true or false