If F(x)= 8sinx/7+cosx then find F'(1) and F'(4pi)
You can use the quotient rule to compute the derivative.
$\displaystyle F(x) = 8 \frac{\sin x}{7 + \cos x} $
$\displaystyle F'(x) = 8 \frac{(7 + \cos x) (cos x) - (sin x) (- sin x)}{(7 + cos x)^2} = 8 \frac{\cos^2 x + 7 \cos x + \sin^2 x} {(7 + \cos x)^2} $
Can you go from here? Do you see anything "special" (think trig) in the numerator of [Math] \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