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(1 +X2) Cos X - Mathematics

(1 +x2) cos x

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Solution

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

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.4 | Q 14 | Page 39
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