If `y={x+sqrt(x^2+a^2)}^n` , then prove that `(dy)/(dx)=(n y)/(sqrt(x^2+a^2))` .

Explanation

To prove that \(\frac{dy}{dx} = \frac{n y}{\sqrt{x^2 + a^2}}\) for \(y = (x + \sqrt{x^2 + a^2})^n\), we will follow these steps:

### Step 1: Rewrite the function
Let \(y = (x + \sqrt{x^2 + a^2})^n\).

### Step 2: Take the natural logarithm
Taking the natural logarithm of both sides, we have:
\[
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