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Use the product and power rules:
[tex]y = (x^2+1)(x^3+1)(x^4+1)[/tex]
The product rule says
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2+1)}{\mathrm dx}(x^3+1)(x^4+1) + (x^2+1)\dfrac{\mathrm d(x^3+1)}{\mathrm dx}(x^4+1) + (x^2+1)(x^3+1)\dfrac{\mathrm d(x^4+1)}{\mathrm dx}[/tex]
and using the power rule to compute the remaining derivatives gives
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \boxed{2x(x^3+1)(x^4+1) + 3x^2(x^2+1)(x^4+1) + 4x^3(x^2+1)(x^3+1)}[/tex]