1. **State the problem:** Find the derivative of the function $$y = (x^{9.6})^{\frac{1}{3}} + 2e^{1.3}$$ with respect to $$x$$. 2. **Simplify the function:** Use the power of a power rule: $$(x^{9.6})^{\frac{1}{3}} = x^{9.6 \times \frac{1}{3}} = x^{3.2}$$. So the function becomes $$y = x^{3.2} + 2e^{1.3}$$. 3. **Recall derivative rules:** - The derivative of $$x^n$$ with respect to $$x$$ is $$nx^{n-1}$$. - The derivative of a constant is 0. 4. **Differentiate each term:** - Derivative of $$x^{3.2}$$ is $$3.2x^{3.2 - 1} = 3.2x^{2.2}$$. - Derivative of $$2e^{1.3}$$ is 0 since $$2e^{1.3}$$ is a constant. 5. **Write the final answer:** $$\frac{dy}{dx} = 3.2x^{2.2}$$ This is the derivative of the given function with respect to $$x$$.