Differentiate the following w.r.t.x. `(sqrt(a^(2)+x^(2))+sqrt(a^(2)-x^(2)))/(sqrt(a^(2)-x^(2))-sqrt(a^(2)-x^(2)))`

Answer

To differentiate the function \( y = \frac{\sqrt{a^2 + x^2} + \sqrt{a^2 - x^2}}{\sqrt{a^2 - x^2} - \sqrt{a^2 - x^2}} \) with respect to \( x \), we first need to simplify the expression.

### Step 1: Simplify the Expression
Notice that the denominator \( \sqrt{a^2 - x^2} - \sqrt{a^2 - x^2} \) simplifies to zero, which means the expression is undefined. Therefore, we need to check if there was a mistake in the question or if we should consider a different approach.

### Step 2: Re-evaluate the Function
Since the denominator is zero, the function does not exist in its current form. We need to ensure that we are working with a valid expression.

### Step 3: Conclusion
Since the expression is undefined due to division by zero, we cannot differentiate it.

### Final Answer
The function is undefined because the denominator is zero.