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log ( 1 √ x ) + 5 x a − 3 a x + 3 √ x 2 + 6 4 √ x − 3 - Mathematics

\[\log\left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}}\] 

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Solution

\[\frac{d}{dx}\left( \log \left( \frac{1}{\sqrt{x}} \right) + 5 x^a - 3 a^x + \sqrt[3]{x^2} + 6 \sqrt[4]{x^{- 3}} \right)\]
\[ = \frac{d}{dx}\left[ log \left( x^\frac{- 1}{2} \right) \right] + 5\frac{d}{dx}\left( x^a \right) - 3\frac{d}{dx}\left( a^x \right) + \frac{d}{dx}\left( x^\frac{2}{3} \right) + 6\frac{d}{dx}\left( x^\frac{- 3}{4} \right)\]
\[ = \frac{d}{dx}\left( \frac{- 1}{2}\log x \right) + 5\frac{d}{dx}\left( x^a \right) - 3\frac{d}{dx}\left( a^x \right) + \frac{d}{dx}\left( x^\frac{2}{3} \right) + 6\frac{d}{dx}\left( x^\frac{- 3}{4} \right)\]
\[ = \frac{- 1}{2} . \frac{1}{x} + 5a x^{a - 1} - 3 a^x \log a + \frac{2}{3} x^\frac{- 1}{3} + 6\left( \frac{- 3}{4} \right) x^\frac{- 7}{4} \]
\[ = \frac{- 1}{2x} + 5a x^{a - 1} - 3 a^x \log a + \frac{2}{3} x^\frac{- 1}{3} - \frac{9}{2} x^\frac{- 7}{4} \]
\[\]

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.3 | Q 16 | Page 34
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