1.

If `log_(10)((x^(3)-y^(3))/(x^(3)+y^(3)))=2`, then `(dy)/(dx)=`A. `(x)/(y)`B. `-(y)/(x)`C. `-(x)/(y)`D. `(y)/(x)`

Answer» Correct Answer - D
Given,
`log_(10)((x^(3)-y^(3))/(x^(3)+y^(3)))=2`
`rArr" "(x^(3)-y^(3))/(x^(3)+y^(3))=10^(2)=100`
`rArrx^(3)-y^(3)=100(x^(3)+y^(3))`
`rArr101y^(3)=-99x^(3)`
On differentiating both sides w.r.t.x, we get
`101xx3y^(2)(dy)/(dx)=-99*(3x^(2))`
`rArr101y^(2)(dy)/(dx)=-99x^(2)`
On multiplying by x both sides, we get
`rArr101xy^(2)(dy)/(dx)=-99x^(3)`
`rArr(dy)/(dx)=(-99x^(3))/(101xy^(2))`
`rArr(dy)/(dx)=(101y^(3))/(101xy^(2))" "[because-99x^(3)=101y^(3)]`
`rArr(dy)/(dx)=(y)/(x)`


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