d \( y=x(2 x+3) \)

To differentiate \( y=x(2x+3) \), we can use the product rule. The product rule states that if you have two functions multiplied together, \( u \) and \( v \), then the derivative is \( u'v + uv' \). Here, let \( u = x \) and \( v = 2x + 3 \). After applying the product rule and simplifying, we find that \( \frac{dy}{dx} = 2x^2 + 3x + 2x = 2x^2 + 5x \). Don’t forget to simplify! A common mistake is to forget to combine like terms after applying rules of differentiation, which can lead to more complex problems down the line. Always double-check your steps to ensure clarity in your final answer.