Soal diferensial. Tentukan diferensial dari soal berikut D[2√x cos(x)]

jawab


y = (2√x) . cos (x)
y = u v

u = 2√x = 2 x^(1/2)
u' = x^(-1/2)
u' = 1/√x ....rasionalkan  1/√x . √x/√x = 1/x √x
u'=1/x √x

v = cos x
v'= - sin x

y' = u' v  +  u v'
y' = (1/x √x) cos x -  (2√x) sin x
y' = 1/x √x ( cos x - 2 x sin x)