anonymous one year ago The function "f" is differentiable and (4f(t)+3t)dt over interval [0,x] = sin(x). Determine f'(π/6).

using $\int_{0}^{x} \ g(t) \ dt = G(x) - G(0)$ meaning $\frac{d}{dx} \int_{0}^{x} \ g(t) \ dt = \frac{d}{dx} [G(x) - G(0)] = g(x)$ we have: $\int_{0}^{x} \ 4f(t) + 3t \ dt = sin(x)$ meaning $\frac{d}{dx} \int_{0}^{x} \ 4f(t) + 3t \ dt = \frac{d}{dx} sin(x)$ and $4f(x) + 3x = cos x$ from that, find $$f'(x)$$ and then $$f'(\pi/6)$$