EXAMPLE 2 Find the derivative of the function below.g(x) = x5 + t4 dt0SOLUTION Since f(t) = 5 + t4 is continuous, Part 1 of the Fundamental Theorem of Calculus gives the answer.

It seems like there's a bit of confusion in your question. The function you've given, g(x) = x^5 + t^4, is a function of two variables, x and t. However, you've also mentioned an integral from 0 to t, which isn't present in the function.

If you want to find the derivative of g(x) = x^5 + t^4 with respect to x, it would simply be 5x^4, as the derivative of t^4 with respect to x is 0 (since t is treated as a constant with respect to x).

If you want to find the derivative of an integral from 0 to x of a function f(t) = 5 + t^4 dt, then by the Fundamental Theorem of Calculus, the derivative would simply be f(x) = 5 + x^4.

Please clarify your question so I can provide a more accurate answer.