Verified answer

G(x) = sqrt(x) - 2exp(x) we can take the sum of derivatives term-wise

G'(x) = x^(1/2) - 2*exp(x) = 1/2(x)^(-1/2) -2exp(x) = 1/(2sqrt(x)) - 2exp(x)

look at sqrt(x) as a form of x^k we know a derivative of this type will be kx^(k-1)

That's exactly what you are doing taking the derivative of x^(1/2) = (1/2)(x^(1/2-1)) 1/2(x^(-1/2)) =

1/2*1/sqrt(x) = 2exp(x) derivative of exp(x) is itself.

So that's how you do it.

Hope this helps.