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ex log a + ea long x + ea log a - Mathematics

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ex log a + ea long x + ea log a

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Solution

\[\frac{d}{dx}\left( e^{x \log a} + e^{a \log x} + e^{a \log a} \right)\]
\[ = \frac{d}{dx}\left( e^{x \log a} \right) + \frac{d}{dx}\left( e^{a \log x} \right) + \frac{d}{dx}\left( e^{a \log a} \right)\]
 `= \frac{d}{dx}\left( e^\log a^x \right) + \frac{d}{dx}\left( {e^\log x}^a \right) + \frac{d}{dx}\left( e^\log a^a \right)`
`= \frac{d}{dx}\left( a^x \right) + \frac{d}{dx}\left( x^a \right) + \frac{d}{dx}\left( a^a \right)`
\[ = a^x \log a + a x^{a - 1} + 0 \]
\[ = a^x \log a + a x^{a - 1}\]

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 30.3 | Q 4 | Page 33

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