Question

Turunan pertama
[tex] \frac{ {x}^{3} - {x}^{2} + 4x }{ {x}^{3} + {x}^{2} - 4x} [/tex]
Mungkin saya akan jarang on brainly ​

Answer 1

Verified answer

Materi : Bentuk Aljabar

f(x) = ( x³ - x² + 4x )/( x³ + x² - 4x )

---

u(x) = x³ - x² + 4x

u'(x) = 3x² - 2x + 4

-

v(x) = x³ + x² - 4x

v'(x) = 3x² + 2x - 4

---

f'(x) = ( u' . v - v' . u )/( v² )

f'(x) = [ ( 3x² - 2x + 4 )( x³ + x² - 4x ) - ( 3x² + 2x - 4 )( x³ - x² + 4x ) ]/[ ( x³ + x² - 4x )( x³ + x² - 4x ) ]

f'(x) = [ 3x⁵ + x⁴ - 10x³ + 12x² - 16x - ( 3x⁵ - x⁴ + 10x³ - 12x² + 16x ) ]/( x⁶ + 2x⁵ - 7x⁴ - 8x³ + 16x² )

f'(x) = [ 3x⁵ + x⁴ - 10x³ + 12x² - 16x - 3x⁵ + x⁴ - 10x³ + 12x² - 16x ]/[ x⁶ + 2x⁵ - 7x⁴ - 8x³ + 16x² ]

f'(x) = [ 2x⁴ - 20x³ + 24x² - 32x ]/[ x⁶ + 2x⁵ - 7x⁴ - 8x³ + 16x² ]

Semoga bisa membantu

[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]