Suppose f (π/3) = 4 and f ' (π/3) = - 5, and let g (x) = f (x) sin (x) and h (x) = cos (x) / f (x). Find the following. g' (π/3) h' (π/3)

Question

Isaiah Santos

Mathematics

8 September, 07:53

Suppose f (π/3) = 4 and f ' (π/3) = - 5, and let g (x) = f (x) sin (x) and h (x) = cos (x) / f (x). Find the following. g' (π/3) h' (π/3)

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Davion Castaneda · Answer 1

Use product rule and quotient rule, respectively. g' (x) = f (x) cos (x) + f' (x) sin (x). Plugging in Pi/3, we get 4 (1/2) + (-5) (sqrt (3) / 2).

For h' (x), we use quotient rule to find that h' (x) = (f (x) * (-sin (x)) - cos (x) * f' (x)) / (f (x)) ^2.

So h' (pi/3) = (4 (-sqrt (3) / 2) - (1/2) (-5)) / 16.