Question

Найдите значение производной в точке Xo

Answer 1

$y=\frac{x^3-1}{x^2}\\\\y'=\frac{3x\cdot x^2-2x(x^3-1)}{x^2}=\frac{3x^3-2x^4+2x}{x^4},\; y'(1)=3\\\\2)\; y=3x^3-12x^2+6x+2\\\\y'=9x^2-24x+6,\; y'(1)=3\\\\3)y=(2x+1)(x-5)=2x^2-9x-5\\\\y'=4x-9,\; y'(2)=-1\\\\4)\; y=2x\cdot cos2x\\\\y'=2\cdot cos2x-4x\cdot sin2x$

$y'(\frac{\pi}{6})=2cos\frac{\pi}{3}-\frac{2\pi }{3}sin\frac{\pi}{3}=2=1-\frac{2\pi }{3}\cdot \frac{\sqrt3}{2}=1-\frac{\pi}{\sqrt3}$