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

Question

s

g(s) = (t − t⁶)⁵dt

2

Answer 1

Since the upper integrand is s and the lower integrand is a constant, g'(s) = f(s) = (s - s⁶)⁵

Answer 2

By FTC part 1, we look at our upper limit of the integral first. We see it's an s. We are going to find the derivative of g(s) by plugging s into everywhere there is a t in the integrand (the expression inside the integral). If we had an upper limit that had something besides a single variable to the first power like an exponential or a root, we would also have to multiply the new expression by the derivative of the upper limit too. We still do technically multiply the expression by the derivative of s in this case, 1.

Our derivative will then be the following:

g'(s) = (s-s⁶)⁵