`"Find "(dy)/(dx)" for "y=log(x+sqrt(a^(2)+x^(2))).`

Explanation

To find \(\frac{dy}{dx}\) for the function \(y = \log\left(x + \sqrt{a^2 + x^2}\right)\), we will follow these steps:

### Step 1: Differentiate the logarithmic function
We start by applying the chain rule for differentiation. The derivative of \(\log(u)\) is given by \(\frac{1}{u} \cdot \frac{du}{dx}\), where \(u = x + \sqrt{a^2 + x^2}\).

\[ \frac{dy}{dx} = \frac{1}{x + \sqrt{a^2 + x^2}} \cdot \frac{d}{dx}\left(x + \sqrt{a^2 + x^2}\right) \]
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