f(x) = (x^{2}+4x+7)^{2 }= u^{2}where we have made u = x^{2}+4x+7. The Chain rule is df(x)/dx = (df(x)/du)(du/dx). df(x)/du = 2u and du/dx = 2x + 4 so therefore df(x)/dx = 2(x^{2}+4x+7)(2x+4).

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