QUESTION9 The derivative of \( y=(x+2)^{5} \) is \( \begin{array}{ll}\text { A. } 5 & \text { B. } 5(x+2)^{4} \\ \text { C. } 5(x+2) & \text { D. } 5 x\end{array} \)

To find the derivative of \( y=(x+2)^{5} \), we can apply the chain rule. According to the chain rule, if \( y = (u)^{n} \) where \( u = x+2 \) and \( n = 5 \), then the derivative \( \frac{dy}{dx} \) is given by \( \frac{dy}{du} \cdot \frac{du}{dx} \). This leads us to \( 5(x+2)^{4} \) as we differentiate. So, the correct answer is B: \( 5(x+2)^{4} \). Now, if you're eager to dive deeper into derivatives, you might look at how they apply in fields like physics, where derivatives help calculate velocity or acceleration. They’re not just a math concept; they are the language of change in the universe! On a lighter note, many students forget to apply the chain rule or mistake it for the product or quotient rules, which can lead to common pitfalls in differentiation. When in doubt, double-check which rule applies and have some fun practicing on different polynomials!