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if sqrt(y)=arctan(x), show that (1+x^2)dy/dx((1+x^2)dy/dx)=2

  • Maths -

    If

    sqrt(y)=arctan(x),

    that means
    y = [arctan(x)]^2

    Let u = arctan x and use the chain rule

    y = u^2
    dy/dx = d(u^2)/du * du/dx
    = 2 arctan(x)/(1 + x^2)
    or
    (1 + x^2)*dy/dx = 2 arctan x = 2 sqrt y

    Are you sure you wrote
    (1+x^2)dy/dx((1+x^2)dy/dx)=2 correctly?
    That has (1+x^2)dy/dx appearing twice in a row. It doesnt look right

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