Задача 32130 y=arctg^(3)(2x-1) найдите производную...

mnuzhnaya

2018-12-19 14:02:53

y=arctg^(3)(2x-1) найдите производную

sova

2018-12-19 14:06:47

★

y`=(u^3)
u=arctg(2x-1)

y`=3u^2*u`

y`=(3arctg^2(2x-1)) * (arctg(2x-1))`=

=(3arctg^2(2x-1))* (1/(1+(2x-1)^2)*(2x-1)`=

=(3arctg^2(2x-1)) * (1/(1+(2x-1)^2)*(2)=

=(6arctg^2(2x-1) )* (1/(1+(2x-1)^2)=

=(6arctg^2(2x-1)) / (1+4x^2-4x+1)=

=(6arctg^2(2x-1)) / (4x^2-4x+2)=

[b]=(3arctg^2(2x-1) )/ (2x^2-2x+1)[/b]