Question

How do you calculate the derivative of `int5(sin(t))^5 dt` from `[e^x,5]`?

Answer 1

`5 d/dx int_(e^x)^5 sin^5 t dt = = -5 e^x sin^5 (e^x)`

Explanation:

`5d/dx int_(e^x)^5 sin^5 t dt = -5 d/dxint_5^(e^x) sin^5 t dt`
`= -5 sin^5 (e^x) d/dx(e^x) = -5 e^x sin^5 (e^x)`