Hi,
There are two terms in the expression.
We can deal with both terms using the fact that
d/dx [ f(x) ]^n = n [ f(x) ]^(n - 1) . f '(x).
Essentially, we
1. bring down the power,
2. reduce the power by 1,
3. differentiate the expression inside the power.
Now d/dx (1 + x^2)^(1/2) = (1/2)(1 + x^2)^(-1/2) .
(2x)
= x / sqrt(1 + x^2), and
d/dx [ x^(-1) ] = -x^(-2).
Combining, we obtain the answer you have computed
previously.
Thanks.
Cheers,
Wen Shih