Найти производную функции (x-2)(x+3)/(x-5). Created by gzm7c. algebra-ru

(x-5)...

gzm7c @gzm7c

August 2022 1 9 Report

Найти производную функции

(x-2)(x+3)/(x-5)

Answers & Comments

sobakazabiyaka

Для начала упростим числитель, чтобы было потом проще считать

$\frac{(x-2)(x+3)}{x-5} =\frac{x^2+3x+x+3}{x-5} =\frac{x^2+4x+3}{x-5}$

$f'(x)=\frac{(x^2+4x+3)'(x-5)-(x^2+4x+3)(x-5)'}{(x-5)^2} =\frac{(2x+4)(x-5)-(x^2+4x+3)*1}{(x-5)^2} =\\ \\ =\frac{2x^2-10x+4x-20-x^2-4x-3}{(x-5)^2} =\frac{x^2-10x-23}{(x-5)^2}$

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