Question

Differentiate \[3^{e^x}\] ?

Answer 1

\[\text{ Let } y = 3^{e^x} \]

\[\text{ Differentiate it with respect to x we get }, \]

\[\frac{d y}{d x} = \frac{d}{dx}\left( 3^{e^x} \right)\]

\[ = 3^{e^x} \log3\frac{d}{dx}\left( e^x \right) \left[ \text{ using chain rule } \right]\]

\[ = e^x \times 3^{e^x} \log3\]

\[So, \frac{d}{dx}\left( 3^{e^x} \right) = e^x \times 3^{e^x} \log3\]