Question

Найдите дифференциал функции
y=$frac{x^{2} +1}{ x^{3} -1}$

y=3^{sin x/ln x}

Answer 1

$y=frac{x^2+1}{x^3-1}\frac{dy}{dx}=frac{(x^2+1)'(x^3-1)-(x^2+1)(x^3-1)'}{(x^3-1)^2}=frac{2x(x^3-1)-3x^2(x^2+1)}{(x^3-1)^2}=\=frac{2x^4-2x-3x^4-3x^2}{(x^3-1)^2}=frac{-x^4-3x^2-2x}{(x^3-1)^2}\\y=3^{frac{sin x}{ln x}}\frac{dy}{dx}=3^{frac{sin x}{ln x}}ln3cdotleft(frac{sin x}{ln x}right)'=3^{frac{sin x}{ln x}}ln3cdotfrac{cos xln x-frac{sin x} x}{ln^2x}=\=3^{frac{sin x}{ln x}}ln3cdotfrac{xcos xln x-{sin x}}{xln^2x}$