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Pick one function below. This is your function y = f(x). y = 2ce² y = r²e² y = √T (a) Find the first derivative f'. (note, you don't have to do this manually. Use wolfram alpha).

Pick one function below. This is your function y = f(x). y = 2ce² y = r²e² y = √T (a) Find the first derivative f'. (note, you don't have to do this manually. Use wolfram alpha).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using the principal of mathematical induction prove the open statements on inductive sets
## Exercise: Derivatives of Functions ### Instructions Pick one function below. This is your function \( y = f(x) \). \( y = 2xe^x \) \( y = x^2 e^x \) \( y = \frac{1}{1-x} \) \( y = \sqrt{x} \) ### Tasks (a) Find the first derivative \( f' \). (Note: you don’t have to do this manually. Use Wolfram Alpha). (b) Find \( f'' \). (c) Find \( f''' \). Make sure to use appropriate tools and techniques for finding derivatives, and check your results for accuracy.
Transcribed Image Text:## Exercise: Derivatives of Functions ### Instructions Pick one function below. This is your function \( y = f(x) \). \( y = 2xe^x \) \( y = x^2 e^x \) \( y = \frac{1}{1-x} \) \( y = \sqrt{x} \) ### Tasks (a) Find the first derivative \( f' \). (Note: you don’t have to do this manually. Use Wolfram Alpha). (b) Find \( f'' \). (c) Find \( f''' \). Make sure to use appropriate tools and techniques for finding derivatives, and check your results for accuracy.
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Thanks for the assistence! I forgot to ask, but how would I make a conjecture for the nth derivative of f using induction?

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