Matematika Jika F(x)=x⁵-1 / x⁴ +3x², maka turunan pertama f'(x)=​

eastonpacochaulv – April 01, 2023

Jika F(x)=x⁵-1 / x⁴ +3x², maka turunan pertama f'(x)=​

Jawab:

Jika F(x)= x⁵-1 / x⁴ +3x², maka turunan pertama f'(x)=​

 

u = x⁵ - 1
u' = 5x

v = x⁴ + 3x²
v' = 4x³ + 6x

[tex]\sf \boxed {f'(x) = \dfrac{u'v - uv'}{v^2}}[/tex]

[tex]\sf f'(x) = \dfrac{5x(x^4+ 3x^2) -(x^5-1)(4x^3 +6x)}{(x^4 + 3x^2)^2}}[/tex]

[tex]\sf f'(x) = \dfrac{5x^5 +15x^3 -(4x^{15} +6x^6 - 4x^3 - 6x)}{(x^4 + 3x^2)^2}}[/tex]

[tex]\sf f'(x) = \dfrac{5x^5 +15x^3 - 4x^{15} - 6x^6 + 4x^3 + 6x}{(x^4 + 3x^2)^2}}[/tex]

[tex]\sf f'(x) = \dfrac{ -4x^{15} - 6x^6+ 5x^5 +19x^3 + 6x}{(x^4 + 3x^2)^2}}[/tex]

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