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X−4 (3 − 4x−5) - Mathematics

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x4 (3 − 4x−5)

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Solution

\[\text{ Let } u = x^{- 4} ; v = 3 - 4 x^{- 5} \]
\[\text{ Then }, u' = - 4 x^{- 5} ; v' = 20 x^{- 6} \]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left[ x^{- 4} \left( 3 - 4 x^{- 5} \right) \right] = x^{- 4} \left( 20 x^{- 6} \right) + \left( 3 - 4 x^{- 5} \right)\left( - 4 x^{- 5} \right)\]
\[ = 20 x^{- 10} - 12 x^{- 5} + 16 x^{- 10} \]
\[ = - 12 x^{- 5} + 36 x^{- 10}\]

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 23 | Page 39

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