1. **State the problem:** Find the derivative of the function $$y = 23x^{9.6} + 2e^{1.3x}$$ with respect to $$x$$. 2. **Recall the formulas:** - The derivative of $$x^n$$ with respect to $$x$$ is $$nx^{n-1}$$. - The derivative of $$e^{kx}$$ with respect to $$x$$ is $$ke^{kx}$$, where $$k$$ is a constant. 3. **Apply the power rule to the first term:** $$\frac{d}{dx} 23x^{9.6} = 23 \times 9.6 x^{9.6 - 1} = 220.8 x^{8.6}$$ 4. **Apply the exponential rule to the second term:** $$\frac{d}{dx} 2e^{1.3x} = 2 \times 1.3 e^{1.3x} = 2.6 e^{1.3x}$$ 5. **Combine the derivatives:** $$\frac{dy}{dx} = 220.8 x^{8.6} + 2.6 e^{1.3x}$$ **Final answer:** $$\boxed{\frac{dy}{dx} = 220.8 x^{8.6} + 2.6 e^{1.3x}}$$