Find each derivative 2) \( y=\tan \left(x^{2}+3 x+2\right) \)

To find the derivative of \( y=\tan \left(x^{2}+3 x+2\right) \), we will use the chain rule. The derivative of \(\tan(u)\) is \(\sec^2(u) \cdot \frac{du}{dx}\), where \( u = x^2 + 3x + 2 \). First, we differentiate \( u \): \[ \frac{du}{dx} = 2x + 3 \] Now we apply the chain rule: \[ \frac{dy}{dx} = \sec^2(u) \cdot \frac{du}{dx} = \sec^2(x^2 + 3x + 2) \cdot (2x + 3) \] Thus, the derivative is: \[ \frac{dy}{dx} = \sec^2(x^2 + 3x + 2) \cdot (2x + 3) \]