Question

Вычислить производную функции

y=2+ x+1/(x-1)²

y=1/√cos4x

Заранее спасибо

Answer 1

y'=((2+(x+1)/(x-1)²)'=(1*(x-1)²-2*(x-1)(x+1))/(x-1)⁴=(x²-2x+1-2*(x²-1))/(x-1)⁴=

(x²-2x+1-2x²+2))/(x-1)⁴=(-x²-2x+3))/(x-1)⁴

y'=(1/√cos4x )'=(1/(cos4x)¹/²)'=(cos4x)⁻¹/²)'=-((0.5(cos4x)⁻³/²*(sin4x))*4=

-(2*sin4x)/((cos4x )*√cos4x)=-2tg4x/√cos4x