1. The problem statement, all variables and given/known data If f(x) = ∫sin x0 √(1+t2)dt and g(y) = ∫3y f(x)dx, find g''(pi/6)? 2. Relevant equations FTC: F(x) = ∫f(x)dx ∫ab f(t)dt = F(b) - F(a) Chain Rule: f(x) = g(h(x)) f'(x) = g'(h(x))h'(x) 3. The attempt at a solution I tried u-substition setting u = tan(x) for the first dirivative with the limits of sine, and it got really weird and bad. I also tried trigonometric substition and I got a similar bad and ugly answer. g'(y) = f(x) = ∫0sin x √(1+t2)dt How do I take the second derivative of g(y)?