1.

If `y=f(x),p=(dy)/(dx) and q=(d^(2)y)/(dx^(2)),` then what is `(d^(2)x)/(dy^(2))` equal to ?A. `-(q)/(p^(2))`B. `-(q)/(p^(3))`C. `(1)/(q)`D. `(q)/(p^(2))`

Answer» Correct Answer - B
As given, `y=f(x), p=(dy)/(dx) and q=(d^(2)y)/(dx^(2))`
`(dx)/(dy)=(1)/(p)rArr(d^(2)x)/(dy^(2))=(-1)/(p^(2)).(dp)/(dy)`
`(dp)/(dx)=(d)/(dx)((dy)/(dx))=(d^(2)y)/(dx^(2))=q`
`(dp)/(dy)=(dp)/(dx).(dx)/(dy)=q.(1)/(p)=(q)/(p)`
`(d^(2)x)/(dy^(2))rArr-(1)/(p^(2))xx(q)/(p)=(-q)/(p^(3))`


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