Question #304842

Find the second derivative of y = (x2+x+1)2


1
Expert's answer
2022-03-03T11:43:38-0500

Solution;

Given;

y=(x2+x+1)2y=(x^2+x+1)^2

dydx=2(x2+x+1)ddx(x2+x+1)\frac{dy}{dx}=2(x^2+x+1)\frac{d}{dx}(x^2+x+1)

y=2(x2+x+1)(2x+1)y'=2(x^2+x+1)(2x+1)

Apply product rule;

y=2(x2+x+1)ddx(2x+1)+2(2x+1)ddx(x2+x+1)y''=2(x^2+x+1)\frac{d}{dx}(2x+1)+2(2x+1)\frac{d}{dx}(x^2+x+1)

y=4(x2+x+1)+2(2x+1)(2x+1)y''=4(x^2+x+1)+2(2x+1)(2x+1)

y=4(x2+x+1)+2(2x+1)2y''=4(x^2+x+1)+2(2x+1)^2





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