Question

производные f(x)=x³/(x²-2x-8)

Answer 1

$f(x)= frac{x^3}{x^2-2x-8}; f'(x)=frac{(x^3)'(x^2-2x-8)-x^3(x^2-2x-8)'}{(x^2-2x-8)^2}= \ = frac{3x^2(x^2-2x-8)-x^3(2x-2)}{(x^2-2x-8)^2}= frac{3x^4-6x^3-24x^2-2x^4+2x^3}{(x^2-2x-8)^2}=\ frac{x^4-8x^3-24}{(x^2-2x-8)^2}=x^2 frac{x^2-8x-24}{((x-4)(x+2))^2}$