**Finding the Derivative of the Function**To find the derivative of the given function, we start with the function provided:\[ f(x) = \sqrt{9 + \sqrt{1 + \sqrt{x}}} \]We need to find the derivative, denoted as \( f'(x) \).1. Let \( u = 1 + \sqrt{x} \).2. Then \( \sqrt{u} = \sqrt{1 + \sqrt{x}} \), and let \( v = \sqrt{u} \). 3. Next, we have \( 9 + v \) inside another root. Let \( w = 9 + v \).The function can now be rewritten in terms of \( w \):\[ f(x) = \sqrt{w} \]The steps to differentiate this function involve using the chain rule multiple times, as well as differentiating square root functions. The completed differentiation process would result in the function \( f'(x) \), which can be placed in the box provided in the image.\[ f'(x) = \]This boxed area serves for the student to either perform their own calculations or check against a step-by-step solution provided in their educational content.No graphs or diagrams are included in the image.

Name: **Finding the Derivative of the Function**To find the derivative of t
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: **Finding the Derivative of the Function**To find the derivative of the given function, we start with the function provided:\[ f(x) = \sqrt{9 + \sqrt{1 + \sqrt{x}}} \]We need to find the derivative, denoted as \( f'(x) \).1. Let \( u = 1 + \sqrt{x}