Using the principal of mathematical induction prove the open statements on inductive sets ## Exercise: Derivatives of Functions### InstructionsPick 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.

Given that Here we need to pick one of the function For that f(x)=x2ex Now we need to derive the…

Answered: Pick one function below. This is your…

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

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.

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