Question

Найти производную 1) y=(5x^2+7x-8)^3 2) y=√8-6x^3 - (все под корнем) 3) y=sin^4(2x)+ctg^2(x/8) , ！

Answer 1

1)
$y=(5x^2+7x-8)^3 \\\\ y'=3(5x^2+7x-8)^2*(10x+7)$

2)
$y=\sqrt{8-6x^3} \\ y'= \frac{-18x^2}{2\sqrt{8-6x^3}} =- \frac{9x^2}{\sqrt{8-6x^3}}$

3)
$y=sin^4(2x)+ctg^2( \frac{x}{8} ) \\\\ y'=4sin^3(2x)*cos(2x)*2+\frac{2ctg(\frac{x}{8} )}{8sin^2(\frac{x}{8})} =8sin^3(2x)*cos(2x)+\\+\frac{ctg(\frac{x}{8} )}{4sin^2(\frac{x}{8})}$