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2 x 2 + 3 x + 4 x - Mathematics

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\[\frac{2 x^2 + 3x + 4}{x}\] 

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Solution

\[\frac{d}{dx}\left( \frac{2 x^2 + 3x + 4}{x} \right)\]
\[ = \frac{d}{dx}\left( \frac{2 x^2}{x} \right) + \frac{d}{dx}\left( \frac{3x}{x} \right) + \frac{d}{dx}\left( \frac{4}{x} \right)\]
\[ = 2\frac{d}{dx}\left( x \right) + 3\frac{d}{dx}\left( 1 \right) + 4\frac{d}{dx}\left( x^{- 1} \right)\]
\[ = 2\left( 1 \right) + 3\left( 0 \right) + 4\left( - 1 \right) x^{- 2} \]
\[ = 2 - \frac{4}{x^2}\]

Concept: The Concept of Derivative - Algebra of Derivative of Functions
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.3 | Q 9 | Page 34

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