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)

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- Mar 13th 2010, 03:50 AMgoaway716help in differentiating
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) - Mar 13th 2010, 04:56 AMskeeter
- Mar 13th 2010, 05:25 AMgoaway716got the first derivative
dy/dx=4cos(x)-9cos(x)/(1+sinx)^2

struggling with the second derivative for the first part of the question - Mar 13th 2010, 05:34 AMe^(i*pi)
Your $\displaystyle f'(x)$ looks fine to me

You can use the quotient rule on the second term.

$\displaystyle u = 9\cos(x) \: \rightarrow \: u' = -9\sin(x)$

$\displaystyle v = [1+sin(x)]^2 \: \: \rightarrow \: v' = 2\cos(x)[1+\sin(x)]$