Solving for f',f'',f''' and determining a general formula

  • Thread starter ttpp1124
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  • #1
ttpp1124
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Homework Statement:
Can someone confirm if my work is correct?
Relevant Equations:
n/a
IMG_4214.jpg
 

Answers and Replies

  • #2
HallsofIvy
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I'm a bit surprised you did not do what you were asked to do! The problem specifically asked you to "find [itex]f'(x)[/itex], [itex]f''(x)[/itex], [itex]f'''(x)[/itex], and [itex]f^{IV}(x)[/itex] then the nth derivative but you have only found [itex]f'(x)[/itex] and [itex]f''(x)[/itex] before jumping to the nth derivative.
Other than the fact that you do not have [itex]f'''(x)= 2^3 e^{2x}[/itex] and [itex]f^{IV}(x)= 2^4e^{2x}[/itex], every thing is good!
 
  • #3
benorin
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The problem also mentions "or ##f^{(n)}\left( \tfrac{1}{2}\right)##", which is of course ##\boxed{f^{(n)}\left( \tfrac{1}{2}\right) = 2^n e}##.
 
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