Задача 31488 Найти y' и y''...

vk459344689

2018-12-02 15:35:25

Найти y' и y''

sova

2018-12-02 15:38:55

★

y`_(x)=y`_(t)/x`_(t)

y`_(t)=(t^(1/5))`=(1/5)*t^((1/5)-1)=(1/5)*t^(-4/5)
x`_(t)=(sqrt(t))`=(t^(1/2))`=(1/2)*t^((1/2)-1)=(1/2)*t^(-1/2)

y`_(x)=(2/5)t^(-4/5)-(-1/2))=(2/5)*t^(-0,3)


y``_(xx)=(y`_(x))`_(t)/x`_(t)

(y`_(x))`_(t)=(2/5)(t^(-0,3))`=(2/5)*(-0,3)*t^(-0,3-1)=(-3/25)*t^(1,3)


y``_(xx)=(-3/25)*t^(1,3) : (1/2)*t^(-1/2) = (-6/25)*t^(1,3-(-1/2))=

=(-6/25)t^(1,8)


О т в е т. y`_(x)=(2/5)*t^(-0,3); y``_(xx)=(-6/25)t^(1,8)