Question

Differentiate \[3^{x^2 + 2x}\] ?

Answer 1

\[\text{Let y} = 3^{x^2 + 2x} \]

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

\[\frac{d y}{d x} = \frac{d}{dx}\left( 3^{x^2 + 2x} \right)\]

\[ = 3^{x^2 + 2x} \times \log_e 3\frac{d}{dx}\left( x^2 + 2x \right) \left[ \text{using chain rule } \right]\]

\[ = \left( 2x + 2 \right) 3^{x^2 + 2x} \log_e 3\]

\[So, \frac{d}{dx}\left( 3^{x^2 + 2x} \right) = \left( 2x + 2 \right) 3^{x^2 + 2x} \log_e 3\]