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Question
\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]
Solution
\[\frac{d}{dx}\left( \frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2} \right)\]
\[ = \frac{1}{3}\frac{d}{dx}\left( x^3 \right) - 2\frac{d}{dx}\left( x^\frac{1}{2} \right) + 5\frac{d}{dx}\left( x^{- 2} \right)\]
\[ = \frac{1}{3}\left( 3 x^2 \right) - 2 . \frac{1}{2} . x^\frac{- 1}{2} + 5\left( - 2 \right) x^{- 3} \]
\[ = x^2 - x^\frac{- 1}{2} - 10 x^{- 3}\]
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