Questions: Specify u and du. (Use symbolic notation and fractions where needed.)

$Specify u and du. (Use symbolic notation and fractions where needed.)$

Transcript text: Specify $u$ and $d u$. (Use symbolic notation and fractions where needed.)

Solution

Solution Steps

To specify $ u $ and $ du $, we need to define a function $ u $ and then find its differential $ du $. The differential $ du $ is given by the derivative of $ u $ with respect to $ x $ multiplied by $ dx $.

Step 1: Define the Variable

We start by defining the variable $ x $.

Step 2: Define the Function $ u $

Next, we define the function $ u $ as $ u(x) $.

Step 3: Calculate the Differential $ du $

To find the differential $ du $, we take the derivative of $ u(x) $ with respect to $ x $ and multiply it by $ dx $: \[ du = \frac{d u(x)}{d x} \cdot dx \]

Final Answer

\[ u = u(x) \] \[ du = dx \cdot \frac{d u(x)}{d x} \]

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