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

Question

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

g(s) = ?

Answer 1

Part 1 of the FTC basically says

d/dx∫_a^x f(t)dt = f(x)

so all you need to do here is replace the variable in the function with the upper integral limit variable.

g'(s) = (s-s⁴)⁶

Note that if the upper limit was a function of s, say h(s), then

g'(s) = (h(s)-h⁴(s))⁶h'(s)

which isn't usually explained in textbooks.