Question

Am I right so far?

G(x)=e^x sqrt(1+x^2)
=e^x(1+x^2)^1/2
=e^x(1/2)(1+x^2)^-1/2(2x) + e^x(1+x^2)^1/2

So I used product rule, chain rule, and exponential function with base e

Answer 1

It's good so far.
You can simplify a little by cancelling the 2's in the numberator and denominator of the first term.