6) If \( f(x)=\frac{\cos x}{1+\sin x} \) then \( f^{\prime}(x) \) \( \begin{array}{ll}\text { (a) } \frac{1}{1+\sin x} & \text { b) } \frac{-1}{1+\sin x}\end{array} \)

\( \int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { \sin x } { 1 + \tan x } d x \)

Let \( f \) be a strictly monotonic differen- tiable function on the closed interval \( [5,10] \) such that \( f(5)=6 \) and \( f(10)= \) 26. Which of the following must be true for the function \( f \) on the interval [5,10]? I. The average rate of change of \( f \) is 4. II. The absolute maximum value of \( f \) is 26 . III. \( f(8)>0 \). (A) I only (B) II only (C) III only (D) I and II (E) I. II. and III

dériver: \( (3-x) e^{x}+1 \)

\( \int \frac { e ^ { - x } } { 1 + e ^ { x } } d x \)

If \( y=2 x y-x^{2}+3 \), then when \( x=1 \), \( \frac{d y}{d x}= \) (A) -6 (B) -2 (C) \( -\frac{2}{3} \) (D) 2 (E) 6