Question

Найдите f'(x) если: а) f(x)=2х-3/х+1 ;

Answer 1

$f(x)= \frac{2x-3}{x+1}$
$( \frac{U}{V} )'= \frac{U'V-UV'}{V^2}$
$f'(x)= \frac{(2x-3)'(x+1)-(2x-3)(x+1)'}{(x+1)^2}$
$f'(x)= \frac{2(x+1)-(2x-3)}{(x+1)^2}$
$f'(x)= \frac{2x+2-2x+3}{(x+1)^2} = \frac{5}{(x+1)^2}$