Second Derivative of e^t + t^e ?

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Homework Help Overview

The discussion revolves around finding the second derivative of the function e^t + t^e, which involves both exponential and polynomial components. Participants are exploring the differentiation process and addressing potential errors in the calculation of derivatives.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the first and second derivatives of the function, with some attempting to clarify the application of differentiation rules. Questions arise regarding the treatment of the exponent in the term t^e and the constants involved in the differentiation process.

Discussion Status

The discussion is ongoing, with participants providing hints and corrections to each other's attempts. There is a recognition of common errors in differentiation, particularly concerning the treatment of constants and exponents. Multiple interpretations of the derivative calculations are being explored.

Contextual Notes

Some participants express uncertainty about the correct application of differentiation rules, particularly in relation to the constant e and its role in the derivatives. There is also a mention of common mistakes that may arise during the differentiation process.

catteyes
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Homework Statement



Find the second derivative of e^t + t^e :


Homework Equations



(e^u) = u' * (e^u)


The Attempt at a Solution



e^t + t^e

1* (e^t) + e*[t^(e-1)]

^^^first derivative

(e^t) + e*e[t^{(e-1)-1}]

^^^ 2nd derivative

Answer?: (e^t) + e^2[t^(e-2)]
 
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catteyes said:
Answer?: (e^t) + e^2[t^(e-2)]

you're quite close. after taking the first derivative, the exponent of t changes, you have not accounted for that.
 
I'm not sure I follow. Doesn't the exponent of t become (e-2) ?
 
d/dt (t^e) = e*t^(e-1)

d/dt (e*t^(e-1)) = ??

EDIT/HINT: Your exponent is correct, it is the constant in front of the exponent that isn't. It's quite a common error, though you probably won't be making it in the future.
 
Last edited:
scratch that... it didn't even look almost right
 
Last edited:
catteyes said:
e^t + t^e

1* (e^t) + e*[t^(e-1)]

[tex]t^e[/tex]
[tex]t^u = u' f'(u)[/tex]

What is u'?
 
u' = e

?

:/
 
catteyes said:
u' = e

?

:/

Wrong, derivative of e^x is e^x; don't confuse that with "e"

hint: e itself is equal to what?
 

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