If `y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y_2+x y_1` is (where `y_r` represents the `r t h` derivative of `y` w.r.t. `xdot` `m^2y` (b) `m y^2` (c) `m^2y^2` (d) none of these

Options

A. `m^(2)y`
B. `my^(2)`
C. `m^(2)y^(2)`
D. none of these

Explanation

We have
`y^(1//m)=(x+sqrt(1+x^(2)))`
`"or "y=(x+sqrt(1+x^(2)))^(m)`
`"or "(dy)/(dx)=m(x+sqrt(1+x^(2)))^(m-1)(1+(x)/(sqrt(x^(2)+1)))`
`=m((x+sqrt(1+x^(2)))^(m))/(sqrt(1+x^(2)))`
`=(my)/(sqrt(1+x^(2)))`
`"or "y_(1)^(2)(1+x^(2))=m^(2)y^(2)`
`"or "2y_(1)y_(2)(1+x^(2))+2xy_(1)^(2)=2m^(2)yy_(1)`
`"or "y_(2)(1+x^(2))+xy_(1)=m^(2)y`