Задача 20264 Y=2+arcsin(sqrt(x)) +(sqrt(x-x^2))...

u1765914539

02.12.2017

Y=2+arcsin(sqrt(x)) +(sqrt(x-x^2))

SOVA

02.12.2017

★

y`=(2+arcsin(√x) +(√x–x^2))` =

=0+(1/sqrt(1-(sqrt(x))^2))* (sqrt(x))`+(1/(2sqrt(x-x^2)))*(x-x^2)`=

=1/(2sqrt(x)*sqrt(1-x))+(1-2x)/(2sqrt(x-x^2))=

=(1+1-2x)/2sqrt(x-x^2)=

=(1-x)/sqrt(x-x^2)=sqrt((1-x)/x)