Question

Carilah turunan
y=[(x^2+1)sinx]^3
Mohon bantuannya

Answer 1

Verified answer

TurunaN Fungsi MaJemuK

y = {(x²+1) sin x} ³

u(x) = (x²+1) sin x
f = x² +1 --> f' = 2x
g = sin x --> g' = cos x
u' = f' g + f g' = 2x sin x + (x²+1) cos x

y = u³
y' = 3 u². u'

y'  = 3 { (x²+1) sin (x)}².{ 2x sin x + (x² + 1) cos x )
y' = 3 (x²+1)² sin² x [ 2x sin x  + (x² +1) cos x ]
y' = 6x (x²+1)² sin³ x +  3(x²+1)³ sin² x cos x