Question

Tolong Bantuannya Kak Jawab Soal Matematika Saya Kak

Answer 1

1. u = 3x² + 1 v = x³ + 2x - 5

u' = 3.2x²⁻¹ v' = 3x³⁻¹ + 2

= 6x = 3x² + 2

y' = u' v + u v'

= 6x( x³ + 2x - 5 ) + ( 3x² + 1 ) ( 3x² + 2 )

= 6x⁴ + 12x² - 30x + 9x⁴ + 9x² + 2

= 15x⁴ + 21x² - 30x + 2

2. u = x² + 3 v = 2x² + 1

u' = 2x²⁻¹ v' = 2.2x²⁻¹

= 2x = 4x

y' = u' v - u v' / v²

Answer 2

Turunan dari

f(x) = axⁿ

= anxⁿ⁻¹

f(x) = (3x²+1)(x³+2x-5)

= 3x²(x³+2x-5) + 1(x³+2x-5)

= 3x⁵+6x³-15x²+x³+2x-5

= 3x⁵+7x³-15x²+2x-5

F'(x) = 15x⁴+21x²-30x+2

f(x) = (x²+3)/(2x²+1)

u = x²+3

u' = 2x

v = 2x²+1

v' = 4x

turunan dari u/v = (u'v-uv')/v²

= (2x(2x²+1)-(x²+3)(4x))/(2x²+1)²

= (4x³+2x-4x³-12x)/(2x²+1)²

= -10x/(2x²+1)²