Question

Найдите производную функции . fx=frac{7-x^3}{5+x^{2}} , x0=-1 .

Answer 1

$f(x)=frac{7-x^3}{5+x^{2}} \ \ f'(x)= frac{(7-x^3)'(5+x^2)-(5+x^2)'(7-x^3)}{(5+x^2)^2} = \ \ frac{-3x^2(5+x^2)-2x(7-x^3)}{(5+x^2)^2} = frac{-3x^4-15x^2-14x+2x^4}{(5+x^2)^2} = \ \ frac{-x^4-15x^2-14x}{(5+x^2)^2} =- frac{x^4+15x^2+14x}{(5+x^2)^2} \ \ f'(-1)=- frac{1+15-14}{(5+1)^2} =- frac{2}{36} =- frac{1}{18}$