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Question Number 108901 by ZiYangLee last updated on 20/Aug/20

$$f\left(x\right)=x^2{(1+x)}^3$$$$\mathrm{Find}{f}^{″}\left(1\right).$$

Answered by malwaan last updated on 20/Aug/20

$$f{}^{\prime }\left(x\right)=x^2\times 3{(1+x)}^2+{(1+x)}^3\times 2x$$$$={(1+x)}^2(3x^2+2x+2x^2)$$$$={(1+x)}^2(5x^2+2x)$$$$\Rightarrow f{}^{″}\left(x\right)={(1+x)}^2(10x+2)+$$$$(5x^2+2x)\left(2\right)(1+x)$$$$\therefore f{}^{″}\left(1\right)=4\times 12+7\times 2\times 2$$$$=48+28=76$$

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