Question

3 Найдите производную функции f(x) = х+3/х-3

Answer 1

Ответ: $=-\frac{6}{(x-3)^2}$

Пошаговое объяснение:

$f(x)=\frac{x+3}{x-3} \\v(x)= x+3 \\ u(x)=x-3\\f'(x)=\frac{v'(x)*u(x)-u'(x)*v(x)}{u(x)^2} \\v'(x)=1 \\u'(x)=1\\= > f'(x)=\frac{1*(x-3)-1*(x+3)}{(x-3)^2} =\frac{-6}{(x-3)^2}$

Answer 2

$f(x) = \frac{x + 3}{x - 3} \\ f'(x) = \frac{(x + 3)'(x - 3) - (x - 3)'(x + 3)}{(x - 3) {}^{2} } = \\ = \frac{x - 3 - (x + 3)}{(x - 3) {}^{2} } = \frac{x - 3 - x - 3}{(x - 3) {}^{2} } = - \frac{6}{(x - 3) {}^{2} }$