f-x-arctan-sinx-and-cosa-2-3-faind-f-a-

Question Number 195136 by mathlove last updated on 25/Jul/23

f (x) = a r c t a n (s i n x)

a n d c o s a = \frac{2}{3} f a i n d f^{^{'}} (a) = ?

Answered by som(math1967) last updated on 25/Jul/23

f^{'} (x) = \frac{1}{1 + {s i n}^{2} x} \times c o s x

f^{'} (α) = \frac{1}{1 + {s i n}^{2} α} \times c o s α

= \frac{1}{1 + \frac{5}{9}} \times \frac{2}{3}

= \frac{9}{14} \times \frac{2}{3} = \frac{3}{7}