If `y=((alphax+beta)/(gammax+delta)),` then `2(dy)/(dx).(d^(3)y)/(dx^(3))` is

Options

A. `7((d^(2)y)/(dx^(2)))^(2)`
B. `5((d^(2)y)/(dx^(2)))^(2)`
C. `3((d^(2)y)/(dx^(2)))^(2)`
D. `((d^(2)y)/(dx^(2)))^(2)`

Answer

C

Explanation

`y=((ax+beta)/(gammax+delta))`
`therefore" "y_(1)=(alpha delta-beta gamma)/((gammax+delta)^(2))`
`y_(2)=(alpha delta-beta gamma)[(-2)/((gamma x+delta)^(3))(gamma)]`
`"and "y_(3)=(alpha delta-beta gamma)[(6)/((gammax+delta)^(4))(gamma^(2))]`
`therefore" "y_(2)^(2)=(2)/(3)y_(1)y_(3)`