If log(10)((x^(3)-y^(3))/(x^(3)+y^(3)))=...

If `log_(10)((x^(3)-y^(3))/(x^(3)+y^(3)))=2`, then `(dy)/(dx)=`

Text Solution

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`log_(10)((x^(3)-y^(3))/(x^(3)+y^(3)))=2`
`therefore (x^(3)-y^(3))/(x^(3)+y^(3))=10^(2)=100`
`thereforex^(3)-y^(3)=100x^(3)+100y^(3)`
`therefore101y^(3)=-99x^(3) thereforey^(3)=(-99)/(101)x^(3)`
Differentiating both sides w.r.t. x, we get,
`3y^(2)(dy)/(dx)=(-99)/(101)xx3x^(2)`
`therefore (dy)/(dx)=-(99x^(2))/(101y^(2))`

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