Question

Задания на производную
4, 8

Answer 1

4)  $y'=( \frac{5}{x}+ \frac{2}{ \sqrt[3]{x^2}})'=- \frac{5}{x^2}+2*(-\frac{2}{3}x^{-\frac{2}{3}-1})=$
$=- \frac{5}{x^2}+\frac{4}{3}x^{-1\frac{2}{3}}=- \frac{5}{x^2}+\frac{4}{3x\sqrt[3]{x^2}};$
8)  $y'=(x( \frac{x}{4}-1)^4)'=$
$=x'( \frac{x}{4}-1)^4+x(( \frac{x}{4}-1)^4)'=( \frac{x}{4}-1)^4+4x( \frac{x}{4}-1)^3(\frac{x}{4})'=$
$=(\frac{x}{4}-1)^4+x(\frac{x}{4}-1)^3=(\frac{x}{4}-1)^3(\frac{x}{4}-1+x)=(\frac{x}{4}-1)^3(1\frac{1}{4}x-1)$