Question

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

Answer 1

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