1. **Problem Statement:** Find the derivative of the function $y = 3x^2 + 5x - 7$. 2. **Formula Used:** The derivative of a function $f(x)$ with respect to $x$ is given by $\frac{dy}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$. 3. **Rules:** - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of a constant is 0. - The derivative of a sum is the sum of the derivatives. 4. **Step-by-step Solution:** - Derivative of $3x^2$ is $3 \times 2x^{2-1} = 6x$. - Derivative of $5x$ is $5$. - Derivative of $-7$ is $0$. 5. **Combine all:** $$\frac{dy}{dx} = 6x + 5 + 0 = 6x + 5$$ 6. **Final Answer:** The derivative of $y = 3x^2 + 5x - 7$ is $$\boxed{6x + 5}$$.