Question

Differentiate `2^(x^3)` ?

Answer 1

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

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

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

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

\[ = 3 x^2 \times 2^{x^3} \times \log_e 2\]

\[\text{ Hence }, \frac{d}{dx}\left( 2^{x^3} \right) = 3 x^2 \times 2^{x^3} \log_e 2\]