Differentiate the following function with respect to (x): (x^3+1)… - Vidyadip

Question

Differentiate the following function with respect to $(\text{x})$:$\frac{(\text{x}^3+1)(\text{x}-2)}{\text{x}^2}$

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Answer

We have,$\frac{\text{d}}{\text{dx}}\frac{(\text{x}^3+1)(\text{x}-2)}{\text{x}^2}$
$=\frac{\text{d}}{\text{dx}}\frac{(\text{x}^4-\text{2x}^3+\text{x}-2)}{\text{x}^2}$
$=\frac{\text{d}}{\text{dx}}(\text{x}^2-2\text{x}+\text{x}^{-1}-\text{2x}^{-2})$
$=\frac{\text{d}}{\text{dx}}(\text{x}^2)-2\frac{\text{d}}{\text{dx}}(\text{x})+\frac{\text{d}}{\text{dx}}(\text{x}^{-1})-2\frac{\text{d}}{\text{dx}}(\text{x}^{-2})$
$=\text{2x}-2-\frac{1}{\text{x}^2}+2.\frac{2}{\text{x}^3}$
$=\text{2x}-2-\frac{1}{\text{x}^2}+\frac{4}{\text{x}^3}$

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