Answer:
[tex]\frac{1}{2^{7}} \frac{1}{\sqrt{e}}[/tex]
Step-by-step explanation:
After derive a couple of times you can see
[tex]f^{n}(x) = \frac{-1^{n+1}}{2^{n}} e^{\frac{-x}{2}}[/tex]
Replacing n by 7 and x by 1 we get
[tex]f^{7}(1) = \frac{-1^{7+1}}{2^{7}} e^{\frac{-1}{2}} = \frac{1}{2^{7}} \frac{1}{\sqrt{e}}[/tex]
