Question

Найти производную функции

Answer 1

$\boxed {\; (x^{n})'=n\cdot x^{n-1}\; }\\\\1)\; \; y=6x^2-\frac{x^3}{3}+5\; \; ,\; \; y'=12x-x^2\\\\2)\; \; y=(x-1)(x^4-3x)\\\\y'=1\cdot (x^4-3x)+(x-1)\cdot (4x^3-3)=x^4-3x+4x^4-3x-4x^3+3=\\\\=5x^4-4x^3-6x-3\\\\3)\; \; y=\frac{4-x}{x}\\\\y'=\frac{-1\cdot x-(4-x)\cdot x}{x^2}=\frac{-x-4x+x^2}{x^2}=\frac{x^2-5x}{x^2}=1-\frac{5}{x}\\\\4)\; \; y=-1,5x^2-\frac{x^3}{6}+\frac{x^4}{4}-10\\\\y'=-3x-\frac{1}{2}\, x^2+x^3$