Answer to Question #304842 in Calculus for jin

Question

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

Answer 1

Solution;

Given;

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

$\frac{dy}{dx}=2(x^2+x+1)\frac{d}{dx}(x^2+x+1)$

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

Apply product rule;

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

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

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