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"If "log(x^(2)+y^(2))=2tan^(-1)""((y)/(x...

`"If "log(x^(2)+y^(2))=2tan^(-1)""((y)/(x))," show that "(dy)/(dx)=(x+y)/(x-y)`

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To solve the problem, we start with the given equation: \[ \log(x^2 + y^2) = 2 \tan^{-1}\left(\frac{y}{x}\right) \] ### Step 1: Differentiate both sides with respect to \(x\) ...
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If log (x^(2)+y^(2))=tan^(-1)((y)/(x)), then show that (dy)/(dx)=(x+y)/(x-y)

If log (x^(2)+y^(2)) = 2 tan ^(-1) (x/y) " then show that " (dy)/(dx) = (y-x)/(y +x)

Knowledge Check

  • If y=log{((1+x)/(1-x))^(1//4)}-(1)/(2)tan^(-1)x," then "(dy)/(dx)=

    A
    `(x)/(1-x^(2))`
    B
    `(x^(2))/(1-x^(4))`
    C
    `(x)/(1+x^(4))`
    D
    `(x)/(1-x^(4))`

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