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

# X3 Ex Cos X - Mathematics

x3 ex cos

#### Solution

$\text{ Let } u = x^3 ; v = e^x ; w = \cos x$
$\text{ Then } , u' = 3 x^2 ; v' = e^x ; w' = - \sin x$
$\text{ Using the product rule }:$
$\frac{d}{dx}\left( uvw \right) = u'vw + uv'w + uvw'$
$\frac{d}{dx}\left( x^3 e^x \cos x \right) = 3 x^2 e^x \cos x + x^3 e^x \cos x + x^3 e^x \left( - \sin x \right)$
$= x^2 e^x \left( 3 \cos x + x \cos x - x \sin x \right)$

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 18 | Page 39