Differentiate the following functions. x^ 4 +x^ 3 +x^ 2 +1 x - Vidyadip

Question

Differentiate the following functions.
$\frac{\text{x}^{4}+\text{x}^{3}+\text{x}^{2}+1}{\text{x}}$

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Answer

$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}^{4}+\text{x}^{3}+\text{x}^{2}+1}{\text{x}}\Big)$
$=\frac{\text{d}}{\text{dx}}\Big(\text{x}^{3}+\text{x}^{2}+\text{x}+\frac{1}{\text{x}}\Big)$
$=3\text{x}^{2}+2\text{x}^{2}+1-\frac{1}{\text{x}^{2}}$
Hence, the required answer is $3\text{x}^{2}+2\text{x}^{2}+1-\frac{1}{\text{x}^{2}}.$

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