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" 3.यदि "y=x^(2)+(1)/(x^(2)+(1)/(x^(2)+....

" 3.यदि "y=x^(2)+(1)/(x^(2)+(1)/(x^(2)+......))" तो सिद्ध कीजिए "(dy)/(dx)=(2xy^(2))/(1+y^(2))" ."

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if y=x^(2)+(1)/(x^(2)+(1)/(x^(2)+............)) then prove that (dy)/(dx)=(2xy^(2))/(1+y^(2))

(dy)/(dx) = (2xy)/(x^(2)-1-2y)

(dy)/(dx) = (2xy)/(x^(2)-1-2y)

(dy)/(dx) = (2xy)/(x^(2)-1-2y)

(dy)/(dx)=(y^(2)+y+1)/(x^(2)+x+1)

(dy)/(dx)=(y^(2)-y+1)/(x^(2)-x+1)

dy/dx=(2xy)/(x^2-1-2y)

xy(dy)/(dx)=(1+y^(2))/(1+x^(2))(1+x+x^(2))

xy(dy)/(dx)=(1+y^(2))/(1+x^(2))(1+x+x^(2))

y(1+x^(2))dy=x(1+y^(2))dx