Hey mikewezyk.
Hint When x = 1, g(x^2+1) = g(1+1) = g(2) = 2 and g'(x^2+1) = g'(1+1) = g'(2) = 4 just as you suspected.
y=f(g(x))-g(x^2+1) at x=1
f(x) = 3 g(x) = 2 f'(x)= -2 g'(x) = 4
I have to find the derivative and use these values to calculate the answer, at x=1.
I go the derivative to be
f'(x)g(x)*g'(x) - g'(x^2+1) *2x (I know this is right)
Plugging in I got -2*2*4 - g'(x^2+1) * 2
The answer is -24 and I have no clue how to evaluate g'(x^2+1), i think it has to evaluate to 4 for the answer to make sense
All help appreciated! Thanks!