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Sin X Cos X - Mathematics

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sin x cos x

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Solution

\[\text{ Let } u = \sin x; v = \cos x\]
\[\text{ Then }, u' = \cos x; v' = - \sin x\]
\[\text{ Using theproduct rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( \sin x \cos x \right) = \sin x \left( - \sin x \right) + \cos x . \cos x\]
\[ = - \sin^2 x + \cos^2 x\]
\[ = \cos 2x\]

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 7 | Page 39

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