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Question
Differentiate \[3^{e^x}\] ?
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Solution
\[\text{ Let } y = 3^{e^x} \]
\[\text{ Differentiate it with respect to x we get }, \]
\[\frac{d y}{d x} = \frac{d}{dx}\left( 3^{e^x} \right)\]
\[ = 3^{e^x} \log3\frac{d}{dx}\left( e^x \right) \left[ \text{ using chain rule } \right]\]
\[ = e^x \times 3^{e^x} \log3\]
\[So, \frac{d}{dx}\left( 3^{e^x} \right) = e^x \times 3^{e^x} \log3\]
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