If show that

Given: y = log[x + √(x² + a²)]

To show:

Proof: y = log[x + √(x² + a²)] …(i)

Let …(ii)

So, eq. (i) becomes

y = log(p) …(iii)

Differentiating eq. (ii) with respect to x, we get

Now, differentiating eq. (iii), we get

Now, substituting the value of p and, we get

…(iii)

Again differentiating with respect to x, we get

[from eq. (iii)]