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  4. If y=(x+1)(x2+1)(x4+1)(x8+1), then displaystyle lim x arrow-1 (d y/d x)=

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Q. If $y=(x+1)\left(x^{2}+1\right)\left(x^{4}+1\right)\left(x^{8}+1\right)$, then $\displaystyle\lim _{x \rightarrow-1} \frac{d y}{d x}=$

TS EAMCET 2019

Solution:

We have,
$y=(x+1)\left(x^{2}+1\right)\left(x^{4}+1\right)\left(x^{8}+1\right)$
$\frac{d y}{d x}=\left(x^{2}+1\right)\left(x^{4}+1\right)\left(x^{8}+1\right)+2 x(x+1)\left(x^{4}+1\right)$
$\left(x^{8}+1\right)+4 x^{3}(x+1)\left(x^{2}+1\right)\left(x^{8}+1\right)+8 x^{7}(x+1) \left(x^{2}+1\right)\left(x^{4}+1\right)$
$\left(\frac{d y}{d x}\right)_{x=-1}=(1+1)(1+1)(1+1)+0+0+0=8$