Find the derivative of d{x^2/(x+1)-(x/(1-x)}/dx

Steps to solve the derivative of d{x^2/(x+1)-(x/(1-x)}/dx

=d{x^2/(x+1)-(x/(1-x)}/dx

=d{x^2/(x+1)}/dx-d{(x/(1-x)}/dx

=[(x+1)(dx^2/dx)-x^2{d(x+1)/dx}]/(x+1)^2-[(x-1)(dx/dx)-x{d(x-1)/dx}]/(x-1)^2

=[(x+1)2x-x^2.1]/(x+1)^2-[(1-x)-x]/(x-1)^2

=(2x^2+2x-x^2)/(x+1)^2-(1-x-x)/(x-1)^2

=(x^2+2x)/(x+1)^2-(1-2x)/(x-1)^2

[On solving]

=(3x^4+x^2-3x^2-1-2x^4-2x^2)/(x^2-1)^2

=(x^4-4x^2-1)/(x^2-1)^2

Hence the derivative of d{x^2/(x+1)-(x/(1-x)}/dx is (x^4-4x^2-1)/(x^2-1)^2

Detail Information:-

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