Question

Find the derivative of the function.

y = integral from cosx to sinx
(ln(8+3v)) dv


lower limit = cosx

upper limit = sinx

y'(x) = ????

Answer 1

Just use Lebniz's Rule:

d/dx ∫[a(x),b(x)] f(t) dt =
f(b(x))b' - f(a(x))a'

d/dx ∫[cosx,sinx] ln(8+3v) dv
= ln(8+3sinx)(cosx) - ln(8+3cosx)(-sinx)