Let `y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda_(z^(3))(dy)/(dz)+z^(4)(d^(2)y)/(dz^(2))`, then the value of `lamda` is

Options

A. 1
B. 2
C. `(1)/(2)`
D. `(1)/(4)`

Explanation

`"We have "(dy)/(dx)=f'(x)and (dx)/(dz)=-(1)/(2^(2)).`
`therefore" "(dy)/(dx)=(dy)/(dz).(dz)/(dx)=-(dy)/(dz).z^(2)`
`rArr" "(d^(2)y)/(dx^(2))=(d)/(dz)[(dy)/(dz).z^(2)](dz)/(dx)`
`=[z^(2)(d^(2)y)/(dz^(2))+(dy)/(dz).2z]z^(2)`
`rArr" "(d^(2)y)/(dx^(2))=z^(4)(d^(2)y)/(dz^(2))+2z^(3)(dy)/(dz)`
`rArr" "lamda=2`