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

# (X + 2)3 - Mathematics

(x + 2)3

#### Solution

$\frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}$
$= \lim_{h \to 0} \frac{\left( x + h + 2 \right)^3 - \left( x + 2 \right)^3}{h}$
$= \lim_{h \to 0} \frac{\left( x + h + 2 - x - 2 \right)\left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]}{h}$
$= \lim_{h \to 0} \frac{h\left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]}{h}$
$= \lim_{h \to 0} \left[ \left( x + h + 2 \right)^2 + \left( x + h + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]$
$= \left[ \left( x + 0 + 2 \right)^2 + \left( x + 0 + 2 \right)\left( x + 2 \right) + \left( x + 2 \right)^2 \right]$
$= \left( x + 2 \right)^2 + \left( x + 2 \right)^2 + \left( x + 2 \right)^2$
$= 3 \left( x + 2 \right)^2$

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 1.11 | Page 25