1. **Stating the problem:** 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 $f'(x) = \frac{d}{dx}f(x)$. 3. **Rules:** - The derivative of $x^n$ is $nx^{n-1}$. - The derivative of a constant times a function is the constant times the derivative of the function. - The derivative of a sum is the sum of the derivatives. 4. **Applying the rules:** - Derivative of $3x^2$ is $3 \times 2x^{2-1} = 6x$. - Derivative of $5x$ is $5 \times 1x^{1-1} = 5$. - Derivative of $-7$ (a constant) 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 $$\boxed{6x + 5}$$.