If `y=1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))+1/(1+x^(b-a)+x^(c-a)),` then `(dy)/(dx)` is equal to (a)`1` (b) `(a+b+c)^(x+b+c-1)` `0` (d) none of these

Explanation

We have given

`y=1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))+1/(1+x^(b-a)+x^(c-a))`

`y=1/(1+(x^(a))/(x^(b))+(x^(c))/(x^(b)))+1/(1+(x^(b))/(x^(c))+(x^(a))/(x^(c)))+1/(1+(x^(b))/(x^(a))+(x^(c))/(x^(d)))`

`y=(x^(b))/(x^(a)+x^(b)+x^(c))+(x^c)/(x^(a)+x^(b)+x^(c))+(x^(a))/(x^(a)+x^(b)+x^(c))`

`y=(x^(b)+x^(c)+x^(a))/(x^(a)+x^(b)+x^(c))=1`

`implies y=1`

`(dy)/(dx)=0`

Hence correct option is (c).