Question

найти производную функции y = (ctg5x)/cos2x

Answer 1

$y^{/} (x)= (frac{ctg 5x}{cos 2x} )^{/}= frac{(ctg 5x)^{/}*cos 2x-ctg5x*(cos 2x)^{/}}{cos ^{2}2x } = \ \ = frac{- frac{5}{sin ^{2} 5x} *cos 2x+2ctg5x*sin 2x}{cos ^{2}2x } = \ = frac{- frac{5cos 2x}{sin ^{2} 5x} + frac{2sin 2x*cos5x}{sin 5x} }{cos ^{2}2x } = frac{- 5cos 2x+2sin 2x*cos5x*sin5x}{sin ^{2} 5x*cos ^{2}2x } = frac{-5cos 2x+sin 2x*sin10x}{ sin ^{2} 5x*cos ^{2}2x }$