If `y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx)` is `(n y)/(sqrt(x^2+a^2))` (b) `-(n y)/(sqrt(x^2+a^2))` `(n x)/(sqrt(x^2+a^2))` (d) `-(n x)/(sqrt(x^2+a^2))`

Options

A. `(ny)/(sqrt(x^(2)+a^(2))`
B. `-(ny)/(sqrt(x^(2)+a^(2))`
C. `(nx)/(sqrt(x^(2)+a^(2))`
D. `-(nx)/(sqrt(x^(2)+a^(2))`

Explanation

To find the derivative \( \frac{dy}{dx} \) of the function \( y = (x + \sqrt{x^2 + a^2})^n \), we will apply the chain rule and the power rule of differentiation. Let's go through the steps one by one.

### Step 1: Identify the function
Given:
\[ y = (x + \sqrt{x^2 + a^2})^n \]

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