F''(x) Second Derivative problem

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Homework Help Overview

The discussion revolves around finding the second derivative of the function f(x) = 3e^(-x²). Participants are engaged in exploring the process of differentiation, specifically focusing on the application of the chain rule and product rule in calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the necessity of first finding the first derivative before proceeding to the second derivative. There is mention of using the chain rule and product rule, with some participants questioning their understanding of these rules.

Discussion Status

Some guidance has been provided regarding the differentiation process, particularly emphasizing the use of the chain rule and product rule. One participant expresses that the information was helpful, indicating progress in their understanding.

Contextual Notes

There are indications of confusion regarding the application of differentiation rules, and participants are working through their understanding of the function's derivatives. The original poster's attempts at the solution suggest a need for clarification on the correct application of calculus principles.

oowhitey
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Homework Statement


find f''(x) <-- second derivative
f(x) = 3e^-x2 <-- that 2 is x squared

Homework Equations





The Attempt at a Solution


my attempt was 6x^2 e^x2
 
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Try taking the first derivative first, then take the second derivative.
 
oowhitey said:

Homework Statement


find f''(x) <-- second derivative
f(x) = 3e^-x2 <-- that 2 is x squared

The Attempt at a Solution


my attempt was 6x^2 e^x2


On the right track, but you're not quite remember your rules correctly.

For the first derivative, use the chain rule. Derivative of the outside 3e^(x^2) times the derivative of the inside (x^2)

Once you've got that, you're going to have a function that is an x times an exponential along the lines of ?xe^(x^2). From there, you need to use the product rule. Which is the derivative of the first function (?x) times the second function (e^(x^2)) plus the first function times the derivative of the second function. Or f'(x)g(x)+f(x)g'(x) (should be familiar from your text) On the derivative of your second function, don't forget the chain rule again!

Hopefully that helps, or if not, that someone can come and correct me.
 
thanks that helped a bunch i think i got it.
 

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