Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Differentiate of the Following from First Principle: − X - Mathematics

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Differentiate  of the following from first principle: 

− x

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Solution

\[\frac{d}{dx}\left( f\left( x \right) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[\frac{d}{dx}\left( - x \right) = \lim_{h \to 0} \frac{- \left( x + h \right) - \left( - x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{- x - h + x}{h}\]
\[ = \lim_{h \to 0} \frac{- h}{h}\]
\[ = \lim_{h \to 0} - 1\]
\[ = - 1\]

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 2.05 | Page 25

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