If `(d^(2)x)/(dy^(2)) ((dy)/(dx))^(3) + (d^(2) y)/(dx^(2)) = k ` , then k is equal to

Options

A. 0
B. 1
C. 2
D. none of these

Answer

A

Explanation

`(dy)/(dx) = ((dx)/(dy))^(-1)`
` rArr (d^(2) y)/(dx^(2)) = - ((dx)/(dy))^(-2) {(d)/(dx)((dx)/(dy))}`
` rArr (d^(2) y)/(dx^(2)) = - ((dx)/(dy))^(-2) {(d)/(dx)((dx)/(dy))(dy)/(dx)}`
`= ((dx)/(dy))^(-2) {(d^(2)x)/(dy^(2)).(dx)/(dy)} = - ((dy)/(dx))^(2)(d^(2) x)/(dy^(2)) `
` rArr (d^(2) x)/(dy^(2) ) + ((dy)/(dx))^(3) (d^(2)x)/(dy^(2)) = 0 `