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If y=tan^(-1){(sqrt(1+x^2)+sqrt(1-x^2))/...

If `y=tan^(-1){(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))}` , `-1 < x < 1, x!= 0 ` . Find `dy/dx`.

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AI Generated Solution

To find \(\frac{dy}{dx}\) for the function \[ y = \tan^{-1}\left(\frac{\sqrt{1+x^2} + \sqrt{1-x^2}}{\sqrt{1+x^2} - \sqrt{1-x^2}}\right), \] we will follow these steps: ...
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Knowledge Check

  • If y= tan^(-1) ""[(sqrt(1+x^2)+ sqrt(1-x^2))/( sqrt(1+x^2)- sqrt(1-x^2))], then (dy)/(dx) equals

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

  • If y=tan^(-1)""(sqrt(1+x^2)-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) , then (dy)/(dx) is equal to

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

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