If `log_(10)((x^(2)-y^(2))/((x^(2))+y^(2)))=2" then "(dy)/(dx)` is equal to

Options

A. `(99x)/(101y)`
B. `(99x)/(101y)`
C. `-(99y)/(101x)`
D. `(99y)/(101x)`

Answer

A

Explanation

Given, `log_(10) ((x^(2)-y^(2))/(x^(2)+y^(2)))=2`
`Rightarrow ((x^(2)-y^(2))/(x^(2)+y^(2)))=10^(2)`
`Rightarrow x^(2)-y^(2)=100(x^(2)+y^(2))`
On differentiating both sides, we get
`2x-2y (dy)/(dx)=100 (2x+2y (dy)/(dx))`
`Rightarrow x-y (dy)/(dx)=100x+100y (dy)/(dx)`
`Rightarrow 101y (dy)/(dx)=-99x`
`Rightarrow (dy)/(dx)=(-99x)/(101f)`