Question

Найдите производную функции y=f(x) в точке x0: f(x)=2/5*x, x0=3 ​

Answer 1

$1.; ; ; f(x)=frac{2}{5}cdot x; ; ,; ; x_0=3\\f'(x)=frac{2}{5}cdot x'=frac{2}{5}cdot 1=frac{2}{5}\\f'(x_0)=f'(3)=frac{2}{5}\\\2.; ; ; f(x)=frac{2}{5x}\\f'(x)=frac{2}{5}cdot (frac{1}{x})'=frac{2}{5}cdot frac{-1}{x^2}=-frac{2}{5x^2}\\f'(3)=-frac{2}{5cdot 3^2}=-frac{2}{5cdot 9}=-frac{2}{45}$