# Differentiate Each of the Following Functions by the Product Rule and the Other Method and Verify that Answer from Both the Methods is the Same. (X + 2) (X + 3) - Mathematics

Differentiate each of the following functions by the product rule and the other method and verify that answer from both the methods is the same.

(x + 2) (x + 3)

#### Solution

${\text{ Product rule } (1}^{st} \text{ method }):$
$\text{ Let } u = x + 2; v = x + 3$
$\text{ Then }, u' = 1; v' = 1$
$\text{ Using the product rule }:$
$\frac{d}{dx}\left( uv \right) = uv' + vu'$
$\frac{d}{dx}\left[ \left( x + 2 \right)\left( x + 3 \right) \right] = \left( x + 2 \right)1 + \left( x + 3 \right)1$
$= x + 2 + x + 3$
$= 2x + 5$
$2^{nd} \text{ method }:$
$\frac{d}{dx}\left[ \left( x + 2 \right)\left( x + 3 \right) \right] = \frac{d}{dx}\left( x^2 + 5x + 6 \right)$
$= 2x + 5$
$\text{ Using both the methods, we get the same answer }.$

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 30.4 | Q 26.2 | Page 39