Find the derivative.

To tackle the problem, we can use the Fundamental Theorem of Calculus, which tells us how to differentiate an integral with variable limits.

So, if we define , according to the theorem, we have:

Calculating this gives us:

Thus, the derivative is:

So the correct answer is .

Now for some added flavor:

In ancient mathematics, the Greeks made significant contributions to the understanding of calculus concepts, even though derivatives were not formally defined until the 17th century. Think of how they used geometric principles to approximate areas and slopes!

For a bit of problem-solving spice, always remember to differentiate the limit function when using the Fundamental Theorem of Calculus. A common mistake is to forget the chain rule when the upper limit is a function of the variable you’re differentiating with respect to. Happy calculating!