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(1 − 2 Tan X) (5 + 4 Sin X) - Mathematics

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(1 − 2 tan x) (5 + 4 sin x)

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Solution

\[\text{ Let } u = 1 - 2 \tan x; v = 5 + 4 \sin x \]
\[\text{ Then }, u' = - 2 \sec^2 x; v' = 4 \cos x\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = u v' + v u'\]
\[\frac{d}{dx}\left[ \left( 1 - 2 \tan x \right)\left( 5 + 4 \sin x \right) \right]\]
\[ = \left( 1 - 2 \tan x \right)\left( 4 \cos x \right) + \left( 5 + 4 \sin x \right)\left( - 2 \sec^2 x \right)\]
\[ = 4 \cos x - 8 \times \frac{\sin x}{\cos x}\cos x - 10 \sec^2 x - 8 \times \frac{\sin x}{\cos^2 x}\]
\[ = 4 \cos x - 8 \sin x - 10 \sec^2 x - 8 \sec x \tan x \]
\[ = 4\left( \cos x - 2 \sin x - \frac{5}{2} \sec^2 x - 2 \sec x \tan x \right)\]

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 13 | Page 39

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