Finding Derivatives of -2z*e^-(z^2)

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Homework Help Overview

The discussion revolves around finding the first and second derivatives of the function -2z*e^-(z^2), which falls under the subject area of calculus, specifically differentiation techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the product rule for differentiation and raise questions about the correct handling of signs in the derivative calculations.

Discussion Status

There is an ongoing exploration of the differentiation process, with participants providing insights and corrections regarding the application of the product rule. Some guidance has been offered on the structure of the derivative, but no consensus has been reached on the final form.

Contextual Notes

Participants are navigating through potential errors in sign and the application of differentiation rules, indicating a focus on understanding the correct approach rather than arriving at a final answer.

T.Engineer
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find the 1st and 2nd derivative of the following equation

-2z*e^-(z^2)
step by step.
Thanks a lot!
 
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Any ideas on this one? if this is a function of z, and you're differentiating with respect to z, does the product rule sound familiar?
 
radou said:
Any ideas on this one? if this is a function of z, and you're differentiating with respect to z, does the product rule sound familiar?

Ok, I get it
it is -2Z (-2z)e^-(z^2) - [e^-(z^2)*(-2)]
and then:
4z^2 * e^-(z^2) + 2e^-(z^2)
Thanks a lot!
 
T.Engineer said:
it is -2Z (-2z)e^-(z^2) ---[/color] [e^-(z^2)*(-2)]

Yep, that's the way to go.
But are you sure about that minus sign?
Can you quote the product rule?
 
CompuChip said:
Yep, that's the way to go.
But are you sure about that minus sign?
Can you quote the product rule?

Oh, I am so sorry it is
-2Z (-2z)e^-(z^2)+ [e^-(z^2)*(-2)]
So, we will have
4z^2*e^-(z^2)-2e^-(z^2)
 
that looks right. Remember, (first) *(derivative of the second) + (second) * (derivative of first). Of course you can change the order, same answer.
 
thanks a lot for all!
 

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