Problem

What is

Solution

To simplify this expression, we'll apply the product rule, the Fundamental Theorem of Calculus, and the chain rule.

First, use the product rule, resulting in

Now the Fundamental Theorem of Calculus. Let the integrand be f(t), an antiderivative be F(t).

Then the above sum equals

Multiply through and simplify to get

The third term in this sum is the derivative of a constant, thus it equals zero. Evaluating the last term using the chain rule, we get all together: