Question

найдите производные заданных функций
f(x)=5-2x⁶/x-x³​

Answer 1

Ответ:

$\displaystyle f'(x) = \frac{6x^8-10x^6+15x^2-5}{(x-x^3)^2}$

Пошаговое объяснение:

$\displaystyle f(x) = \frac{5-2x^6}{x-x^3}$

$\displaystyle f'(x) = \frac{(5-2x^6)'*(x-x^3)-(x-x^3)'*(5-2x^6)}{(x-x^3)^2}$

$\displaystyle f'(x) = \frac{-12x^5*(x-x^3)-(1-3x^2)*(5-2x^6)}{(x-x^3)^2}$

$\displaystyle f'(x) = \frac{-12x^6+12x^8-(5-2x^6-15x^2+6x^8)}{(x-x^3)^2}$

$\displaystyle f'(x) = \frac{-12x^6+12x^8-5+2x^6+15x^2-6x^8}{(x-x^3)^2}$

$\displaystyle f'(x) = \frac{6x^8-10x^6+15x^2-5}{(x-x^3)^2}$