\[ =\left(\frac{1 / 2}{x+9}\right)^{-1 / 2}\left(\frac{9}{(x+9)^{2}}\right) \] Therefore, we have the following result. \( y^{\prime}=\square \)
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This expression is related to calculus and specifically deals with the differentiation of complex functions. It showcases the application of the chain rule and power rule, often encountered in calculus courses when tackling derivatives of functions involving roots and rational expressions. Understanding these rules is foundational for solving more complex problems in higher-level mathematics and physics. In practical terms, mastering this kind of differentiation can aid in various fields, such as engineering, economics, and even computer graphics. Whether it’s optimizing a function to maximize profit or designing a smooth curve, these calculus principles help solve real-world problems efficiently, demonstrating the importance of mathematics in everyday decision-making and technological advancement.