Question
Differentiate the following function with respect to $(\text{x})$:

$\frac{\text{x}^3}{3}-2\sqrt{\text{x}}+\frac{5}{\text{x}^2}$

Answer

We have to differentiate $\text{f}(\text{x})$ with respect to $\text{x}$

$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}^3}{3}-2\sqrt{\text{x}}+\frac{5}{\text{x}^2}\Big)$

$\frac{1}{3}\frac{\text{d}}{\text{dx}}(\text{x}^3)-2\frac{\text{d}}{\text{dx}}\sqrt{\text{x}}+5\frac{\text{d}}{\text{dx}}(\text{x}^{-2})$

$=\frac{1}{3}.3\text{x}^2-2\frac{1.1}{2\sqrt{\text{x}}}+5.(-2)\text{x}^{-3}$

$=\text{x}^2-\text{x}^{-\frac{1}{2}}-10\text{x}^{-3}$

$=\text{x}^2-\frac{1}{\sqrt{\text{x}}}-\frac{10}{\text{x}^3}$

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