$\begin{align}  & \text{Method 1} \\ & \text{Let }y=(2x+1)(3x+1) \\ & y=6{{x}^{2}}+5x+1 \\ & \frac{dy}{dx}=\frac{d}{dx}\left( 6{{x}^{2}}+5x+1 \right)=12x+5 \\ & \text{Method 2} \\ & \text{Using the product rule} \\ & \frac{dy}{dx}=u\frac{dv}{dx}+v\frac{du}{dx} \\ & \frac{dy}{dx}=(2x+1)\frac{d}{dx}(3x+1)+(3x+1)\frac{d}{dx}(2x+1) \\ & \frac{dy}{dx}=(2x+1)(3)+(3x+1)(2)=12x+5 \\\end{align}$