Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Question

g(s) =8 --)S (t-t^4)^9 dt

g'(s) = ?

Answer 1

If c is a constant and if f(x) = ∫_{(c to x)} h(t)dt, then, by the Fundamental Theorem of Calculus,

f'(x) = h(x).

So, for g(s) = ∫_{(8 to s)} (t - t⁴)⁹, g'(s) = (s - s⁴)⁹.