Question

КОШМАР НА УЛИЦЕ АЛГЕБРЫ!

Answer 1

$1)y=\frac{1}{Cos^{6}5x } =Cos^{-6}5x=-6Cos^{-7}5x*(Cos5x)'*5=\\\\=-30Cos^{-7} 5x*(-Sin5x)=\boxed{\frac{30Sin5x}{Cos^{7}5x }}$

$2)y=4Sin\alpha+2Ctg\alpha-4arcCos\alpha\\\\y'=4(Sin\alpha)'+2(Ctg\alpha)'-4(arcCos\alpha)'=\\\\=4Cos\alpha+2*(-\frac{1}{Sin^{2}\alpha} ) -4*(-\frac{1}{\sqrt{1-\alpha ^{2}} } )=\\\\=\boxed{4*Cos\alpha -2*\frac{1}{Sin^{2} \alpha }+4*\frac{1}{\sqrt{1-\alpha^{2} }}}$