(B) To find the derivative of $e^{x^3}$ with respect to $x$,we use the chain rule.Let $y = e^{x^3}$.By the chain rule,$\frac{dy}{dx} = \frac{d}{dx}(e^

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(B) To find the derivative of $e^{x^3}$ with respect to $x$,we use the chain rule.Let $y = e^{x^3}$.By the chain rule,$\frac{dy}{dx} = \frac{d}{dx}(e^{x^3}) = e^{x^3} \cdot \frac{d}{dx}(x^3)$.Since $\frac{d}{dx}(x^3) = 3x^2$,we have:$\frac{dy}{dx} = e^{x^3} \cdot 3x^2 = 3x^2e^{x^3}$.Thus,the correct option is $B$.