Задача 28777 Как это решать?...
Условие
математика
482
Решение
★
z`_(y)=z`_(u)*u`_(y)+z`_(v)*v`_(y)
z`_(u)=(arcsinu^3v^5)`_(u)=(u^3*v^5)`_(u)/sqrt(1-(u^3v^5)^2)=
=3u^2v^5/sqrt(1-u^6v^(10));
z`_(v)=(arcsinu^3v^5)`_(v)=(u^3*v^5)`_(v)/sqrt(1-(u^3v^5)^2)=
=5u^3v^4/sqrt(1-u^6v^(10));
u`_(x)=(e^(2x+y))`_(x)=e^(2x+y)*(2x+y)`_(x)=
=e^(2x+y)*2=2*e*(2x+y)
u`_(y)=(e^(2x+y))`_(y)=e^(2x+y)*(2x+y)`_(y)=
=e^(2x+y)*1=e^(2x+y)
v`(x)=(cosx-siny)`_(x)=-sinx+0=-sinx
v`(y)=(cosx-siny)`_(y)=0-cosy=-cosy
О т в е т.
z`_(x)=(6u^2v^5*e*(2x+y))/sqrt(1-u^6v^(10))+
+(5u^3v^4*e^(2x+y))/sqrt(1-u^6v^(10))
z`_(y)=(-3*u^2*v^5*sinx)/sqrt(1-u^6v^(10))-
(5u^3*v^4*cosy)/sqrt(1-u^6v^(10))