Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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2 X - Mathematics

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\[\frac{2}{x}\]

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Solution

\[\left( i \right) \frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\frac{2}{x + h} - \frac{2}{x}}{h}\]
\[ = \lim_{h \to 0} \frac{2x - 2x - 2h}{hx(x + h)}\]
\[ = \lim_{h \to 0} \frac{- 2h}{hx(x + h)}\]
\[ = \lim_{h \to 0} \frac{- 2}{x(x + h)}\]
\[ = \frac{- 2}{x^2}\]

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 30.2 | Q 1.01 | Page 25

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