function f is defined by f(x)=4sin(x)+9/(1+sin(x)) with 0<=x<=pi
1)Evaluate the first and second derivative of f.
2)Find and classify the stationary points of the funtion
3)Find the greatest and least values of f(x)
Your $\displaystyle f'(x)$ looks fine to me
You can use the quotient rule on the second term.
$\displaystyle u = 9\cos(x) \: \rightarrow \: u' = -9\sin(x)$
$\displaystyle v = [1+sin(x)]^2 \: \: \rightarrow \: v' = 2\cos(x)[1+\sin(x)]$