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

# Differentiate of the Following from First Principle: − X - Mathematics

Differentiate  of the following from first principle:

− x

#### 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