1. **State the problem:** Find the first derivative of the function $$y(x) = k e^{x^3} + f$$ with respect to $$x$$. 2. **Recall the chain rule:** If $$y = g(h(x))$$, then $$\frac{dy}{dx} = g'(h(x)) \cdot h'(x)$$. 3. **Identify the outer and inner functions:** Here, $$g(u) = k e^u$$ and $$h(x) = x^3$$. 4. **Differentiate the outer function:** $$g'(u) = k e^u$$. 5. **Differentiate the inner function:** $$h'(x) = 3x^2$$. 6. **Apply the chain rule:** $$\frac{dy}{dx} = g'(h(x)) \cdot h'(x) + \frac{d}{dx}f = k e^{x^3} \cdot 3x^2 + 0$$ 7. **Simplify the expression:** $$\frac{dy}{dx} = 3k x^2 e^{x^3}$$ **Final answer:** $$\boxed{\frac{dy}{dx} = 3k x^2 e^{x^3}}$$