Question

найти производную функцию​

Answer 1

Ответ:

$\boxed{\bigg ( \dfrac{5x^{3}}{(4 - x)^{2}} \bigg)' = \dfrac{5x^{2}(12 - x)}{(4 - x)^{3}}}$

Объяснение:

$\bigg ( \dfrac{5x^{3}}{(4 - x)^{2}} \bigg)' = \dfrac{(5x^{3})'(4 - x)^{2} - 5x^{3}(4 - x)^{2}'}{(4 - x)^{4}} = \dfrac{15x^{2} (4 - x)^{2} + 10x^{3}(4 - x)}{(4 - x)^{4}} =$

$= \dfrac{(4 - x)(15x^{2} (4 - x)+10x^{3})}{(4 - x)(4 - x)^{3}} = \dfrac{60x^{2} - 15x^{3} + 10x^{3}}{(4 - x)^{3}} = \dfrac{60x^{2} - 5x^{3}}{(4 - x)^{3}} = \dfrac{5x^{2}(12 - x)}{(4 - x)^{3}}$