Question

PLEASE HELP! ASAP! MEDAL!

Answer 1

I got -1 for the first one, but I have a feeling that is it is incorrect because I got it too easily.

Answer 2

\(\large\color{black}{ \displaystyle \frac{d}{dx}\left[~f(g(x)~\right]=f'(g(x))\times g'(x) }\)

Now, at x=2,

\(\large\color{black}{ \displaystyle f'(g(x))\times g'(x)=f'(2) \times (-3)=(1/3) \times (-3)=-1}\)

Answer 3

yes, -1 is right.
Honestly this is the first time I ever do such a question. Just another manipulation I have seen:)

Answer 4

\(\large\color{black}{ \displaystyle \frac{d}{dx}~\sqrt{f(x) }~=\frac{f'(x) }{2\sqrt{f(x) }}=\frac{1/3}{2\sqrt{8}} }\)

Answer 5

the last step in that line is also based on the fac that you are evaluating the expression at x=2.

Answer 6

Questions?

Answer 7

I'm confused about the second one.

Answer 8

How did you get