A friend tells you that $\displaystyle {\left({\left[{f{{\left({x}\right)}}}\right]}^{{n}}\right)}'={n}{\left[{f}'{\left({x}\right)}\right]}^{{{n}-{1}}}$, so the derivative of a power is a power of the derivative.

Let $\displaystyle {f{{\left({x}\right)}}}={8}{x}+{7}$ and consider the function $\displaystyle {y}={\left[{f{{\left({x}\right)}}}\right]}^{{2}}$.

$\displaystyle {f}'{\left({x}\right)}=$Preview Question 6 Part 1 of 5  

$\displaystyle {2}{\left[{f}'{\left({x}\right)}\right]}^{{{1}}}=$Preview Question 6 Part 2 of 5  

$\displaystyle {\left[{f{{\left({x}\right)}}}\right]}^{{2}}=$Preview Question 6 Part 3 of 5  

$\displaystyle {\left({\left[{f{{\left({x}\right)}}}\right]}^{{2}}\right)}'=$Preview Question 6 Part 4 of 5  

Based on your work above (check all that apply):