hitung turunan dari [tex]y = 5x( {x}^{3} - 1) ^{4} [/tex]

jawab


y =  5x . (x³ - 1)⁴

y = uv
y' = u'v + uv'

y' = 5(x³ -1)⁴+  (5x)(4)(3x²)(x³ -1)³
y' = 5(x³ -1)⁴ + 60x² (x³ -1)³
y' = 5(x³-1)³ ( x³ -1 + 60x²)
y' = 5(x³-1)³ (x³ + 60 x² - 1)

[tex]y = 5x( {x}^{3} - 1) ^{4} [/tex]
gunukan aturan parsial

misalnya

u = 5x ==>>> u' = 5

[tex]v = ({x}^{3} - 1) ^{4}[/tex]
[tex] {v}^{1} = 4( {x}^{3} - 1 {)}^{3} 3 {x}^{2} \\ {v}^{1} = 12 {x}^{2} ( {x}^{3} - 1 {)}^{3} [/tex]
y' = u' v + u v'

[tex] = 5( {x}^{3} - 1 {)}^{4} + 5x.12x^{2} ( {x}^{3} - 1 {)}^{3} \\ \\ = 5( {x}^{3} - 1 {)}^{4} + 60 {x}^{2} ( {x}^{3} - 1 {)}^{3} [/tex]
semoga paham dan bisa dijabarkan...