Find `(dy)/(dx)` if, `tan^(-1)(x^2+y^2)=a`

Answer

N/a

Explanation

We have, `tan^(-1)(x^(2)+y^(2))=a`
On differentiating both sides w.r.t.x, we get
`(d)/(dx) tan^(-1) (x^(2)+y^(2)) = d/(dx) (a)`
`rArr (1)/(1+(x^(2)+y^(2))^(2)).(d)/(dx) (x^(2)+y^(2)) = 0`
`rArr 2x + (d)/(dy)y^(2).(dy)/(dx) = 0`
`rArr 2y.(dy)/(dx) = - 2x`
`:. (dy)/(dx) = (-2x)/(2y) = (-x)/(y)`