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$\frac{x^{4}+x^{3}+x^{2}+1}{x}$

Question.

$\frac{x^{4}+x^{3}+x^{2}+1}{x}$

solution:

Let $y=\frac{x^{4}+x^{3}+x^{2}+1}{x}$

$\Rightarrow$$y=\frac{x^{4}+x^{3}+x^{2}+1}{x}$

Dividing by $x$ we get

$\Rightarrow$$y=x^{3}+x^{2}+x+\frac{1}{x}$

Differentiating given equation with respect to $x$

$\Rightarrow$$\frac{d y}{d x}=\frac{d}{d x}\left(x^{3}+x^{2}+x+\frac{1}{x}\right)$

On differentiation we get

$\Rightarrow$$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{x}^{3}+\mathrm{x}^{2}+\mathrm{x}+\frac{1}{\mathrm{x}}\right)=3 \mathrm{x}^{2}+2 \mathrm{x}+1-\frac{1}{\mathrm{x}^{2}}$

$\Rightarrow$$\frac{d y}{d x}=\frac{d}{d x}\left(x^{3}+x^{2}+x+\frac{1}{x}\right)$

On differentiation we get

$\Rightarrow$$\frac{d}{d x}\left(x^{3}+x^{2}+x+\frac{1}{x}\right)=3 x^{2}+2 x+1-\frac{1}{x^{2}}$

Hence, the required answer is $3 \mathrm{x}^{2}+2 \mathrm{x}+1-1 / \mathrm{x}^{2}$

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