### Finding the Derivative of the Function**Problem Statement:**Find the derivative of the function \( y = 9 \sec^{-1} (x + 5) \).**Instructions:** Use symbolic notation and fractions where needed.**Solution:**\[y' = \boxed{}\]In this context, \( \sec^{-1} \) denotes the inverse secant function. To find the derivative, apply the chain rule and the derivative formula for the inverse secant function:The derivative of \( \sec^{-1}(x) \) is \( \frac{d}{dx}[\sec^{-1}(x)] = \frac{1}{|x|\sqrt{x^2 - 1}} \).For the function \( y = 9 \sec^{-1} (x + 5) \), we let \( u = x + 5 \), then the derivative of \( y \) with respect to \( x \) is given by:\[\frac{dy}{dx} = 9 \cdot \frac{d}{du}[\sec^{-1}(u)] \cdot \frac{du}{dx}\]Substitute \( u = x + 5 \):\[\frac{dy}{dx} = 9 \cdot \frac{1}{|x + 5| \sqrt{(x + 5)^2 - 1}} \cdot 1\]So the final expression for \( y' \) is:\[y' = \frac{9}{|x + 5| \sqrt{(x + 5)^2 - 1}}\]Therefore, the solution is:\[y' = \boxed{\frac{9}{|x+5| \sqrt{(x+5)^2 - 1}}}\]

Name: ### Finding the Derivative of the Function**Problem Statement:**Find
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: ### Finding the Derivative of the Function**Problem Statement:**Find the derivative of the function \( y = 9 \sec^{-1} (x + 5) \).**Instructions:** Use symbolic notation and fractions where needed.**Solution:**\[y' = \boxed{}\]In this context, \( \s