Question

Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(s) = s (t â t2)6dt 5

Answer 1

Assuming it's

$g(s)=\displaystyle\int_5^s(t-t^2)^6\,\mathrm dt$

By the FTC, we have

$\dfrac{\mathrm dg}{\mathrm ds}=(s-s^2)^6\cdot\dfrac{\mathrm d}{\mathrm ds}s=(s-s^2)^6$