You can use the quotient rule to compute the derivative.

Can you go from here? Do you see anything "special" (think trig) in the numerator of [tex] \frac{\cos^2 x + 7 \cos x + \sin^2 x} {(7 + \cos x)^2} [/tex] ??

Try to finish this. If you have further questions, don't hesitate to ask.

-Andy