Question

Помогите пожалуйста с решением

Answer 1

$1); ; f(x)= frac{x^6}{6}+5x^4-ctgx+sqrt7x\\f'(x)=x^5+20x^3+frac{1}{sin^2x} +sqrt7\\2); ; y=arcsinfrac{2x^3}{1+x^6}\\y'= frac{1}{sqrt{1-frac{4x^6}{(1+x^6)^2}}}cdot frac{6x^2(1+x^6)-2x^3cdot 6x^5}{(1+x^6)^2}=frac{1}{sqrt{frac{(1-x^6)^2}{(1+x^6)^2}}}cdot frac{6x^2(1-x^6)}{(1+x^6)^2}=\\= frac{1+x^6}{1-x^6}cdot frac{6x^2(1-x^6)}{(1+x^6)^2} = frac{6x^2}{1+x^6}$