Question

Nomer 11 yaaaa turunan fungsi trigonometri

Answer 1

Verified answer

F(x) = (sin x - cos x)/(tan x) = u/v
u = sin x - cos x => u' = cos x + sin x
v = tan x => v' = sec^2 x
f'(x) = (u' v - v' u) / v^2
f'(x) = ((cos x + sin x)(Tan x) - (sec^2 x) (sin x - cos x)) / (tan x)^2
f'(45°)
= ((cos 45° + sin 45°)Tan 45° - (sec 45°)^2 (sin 45° - cos 45°)) / (Tan 45°)^2
= ((1/2 √2 + 1/2 √2) (1) - (√2)^2 (1/2 √2 - 1/2 √2)) / (1)^2
= (√2 - 2(0)) / 1
= √2