Differentiate. \[ y=\left(5 x^{2}+6\right)(2 x+3) \]

To differentiate the function \( y=(5 x^{2}+6)(2 x+3) \), we can use the product rule, which states that if you have a product of two functions \( u(x) \) and \( v(x) \), then the derivative \( y' \) is given by: \[ y' = u'v + uv' \] Here, let \( u = 5x^2 + 6 \) and \( v = 2x + 3 \). First, we find the derivatives: 1. \( u' = \frac{d}{dx}(5x^2 + 6) = 10x \) 2. \( v' = \frac{d}{dx}(2x + 3) = 2 \) Now, we apply the product rule: \[ y' = u'v + uv' = (10x)(2x + 3) + (5x^2 + 6)(2) \] Now we simplify each part: 1. \( 10x(2x + 3) = 20x^2 + 30x \) 2. \( (5x^2 + 6)(2) = 10x^2 + 12 \) Now, combine both expressions: \[ y' = (20x^2 + 30x) + (10x^2 + 12) = 30x^2 + 30x + 12 \] So, the derivative of the given function is: \[ y' = 30x^2 + 30x + 12 \]