Question

Y=x + sin x per 1+cos x,berapakah nilai y'(y aksen)??

pake caranya ya kak

Answer 1

U = x + sin x => u' = 1 + cos x
v = 1 + cos x => v' = -sin x
y = u/v maka y' = (u'.v - v'.u)/v^2
= [(1 + cos x)(1 + cos x) - (-sin x)(x + sin x)] / (1 + cos x)^2
= [1 + 2cos x + cos^2 x + x sin x + sin^2 x] / (1 + cos x)^2
= [2 + 2 cos x + x sin x] / (1 + cos x)^2
atau
= (2 + 2 cos x + x sin x) / (1 + 2 cos x + cos^2 x)