- #1
ttpp1124
- 110
- 4
- Homework Statement
- Can someone confirm if my work is correct?
- Relevant Equations
- n/a
Solving for f',f'',f''' and determining a general formula
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SUMMARY
The discussion focuses on calculating the derivatives of the function f(x), specifically f'(x), f''(x), f'''(x), and f^{IV}(x), as well as deriving a general formula for the nth derivative. The correct expressions are f'''(x) = 2^3 e^{2x} and f^{IV}(x) = 2^4 e^{2x}. Additionally, the nth derivative evaluated at x = 1/2 is confirmed to be f^{(n)}(1/2) = 2^n e. The importance of following the problem's instructions closely is emphasized.
PREREQUISITES- Understanding of calculus, specifically differentiation
- Familiarity with exponential functions
- Knowledge of notation for derivatives, including nth derivatives
- Basic algebra skills for manipulating expressions
- Study the rules of differentiation for exponential functions
- Learn how to derive higher-order derivatives systematically
- Explore the concept of Taylor series and its relation to derivatives
- Investigate applications of nth derivatives in real-world problems
Students and educators in calculus, mathematicians focusing on differential equations, and anyone interested in advanced derivative calculations.
- #2
HallsofIvy
Science Advisor
Homework Helper
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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!
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
Science Advisor
- 1,442
- 191
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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