Question
Differentiate the following function with respect to $(\text{x})$:$\frac{(\text{x}+5)(\text{2x}^2-1)}{\text{x}}$
✓
Answer
We have,$\frac{\text{d}}{\text{dx}}\Big\{\frac{(\text{x}+5)(\text{2x}^2-1)}{\text{x}}\Big\}$
$=\frac{\text{d}}{\text{dx}}\Big(\frac{\text{2x}^3+\text{10x}^2-\text{x}-5}{\text{x}}\Big)$
$=\frac{\text{d}}{\text{dx}}(\text{2x}^2+\text{10x}-1-5\text{x}^{-1})$
$=2\frac{\text{d}}{\text{dx}}(\text{x}^2)+10\frac{\text{d}}{\text{dx}}(\text{x})-\frac{\text{d}}{\text{dx}}(1)-5\frac{\text{d}}{\text{dx}}(\text{x}^{-1})$
$=2\times2\text{x}+10-0+\frac{5}{\text{x}^2}$
$=4\text{x}+10+\frac{5}{\text{x}^2}$
$=\frac{\text{d}}{\text{dx}}\Big(\frac{\text{2x}^3+\text{10x}^2-\text{x}-5}{\text{x}}\Big)$
$=\frac{\text{d}}{\text{dx}}(\text{2x}^2+\text{10x}-1-5\text{x}^{-1})$
$=2\frac{\text{d}}{\text{dx}}(\text{x}^2)+10\frac{\text{d}}{\text{dx}}(\text{x})-\frac{\text{d}}{\text{dx}}(1)-5\frac{\text{d}}{\text{dx}}(\text{x}^{-1})$
$=2\times2\text{x}+10-0+\frac{5}{\text{x}^2}$
$=4\text{x}+10+\frac{5}{\text{x}^2}$
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