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

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

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

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

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

=xcosx+sinx-[{(1-x^2)e^x-e^x(0+x^2)}/(1+x^2)^2]

=xcosx+sinx-[e^x{(1-x^2)-(0+x^2)}/(1+x^2)^2]

=xcosx+sinx-[e^x(1-x)^2/(1+x^2)^2}

Hence the derivative of xsinx-e^x/(1+x^2) is xcosx+sinx-[e^x(1-x)^2/(1+x^2)^2}

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