Questions: Find the differential of the function y = √(4+x). dy=

Transcript text: Find the differential of the function $y=\sqrt{4+x}$. \[ d y= \]

Solution

Solution Steps

To find the differential of the function $ y = \sqrt{4 + x} $, we need to compute the derivative of $ y $ with respect to $ x $ and then multiply it by $ dx $. The derivative of $ y $ can be found using the chain rule.

Step 1: Define the Function

We start with the function $ y = \sqrt{4 + x} $.

Step 2: Compute the Derivative

To find the differential, we first need to compute the derivative of $ y $ with respect to $ x $. Using the chain rule, we get: \[ \frac{dy}{dx} = \frac{1}{2\sqrt{4 + x}} \]

Step 3: Multiply by $ dx $

The differential $ dy $ is obtained by multiplying the derivative by $ dx $: \[ dy = \frac{1}{2\sqrt{4 + x}} \, dx \]