Differentiate the following functions. (x+1 x )^ 3 - Vidyadip

Question

Differentiate the following functions.
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^{3}$

✓

Answer

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

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