• Support PF! Buy your school textbooks, materials and every day products Here!

Second Derivative of e^t + t^e ?

  • Thread starter catteyes
  • Start date
  • #1
9
0

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)]
 

Answers and Replies

  • #2
1,033
1
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.
 
  • #3
9
0
I'm not sure I follow. Doesn't the exponent of t become (e-2) ?
 
  • #4
1,033
1
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:
  • #5
9
0
scratch that... it didn't even look almost right
 
Last edited:
  • #6
1,291
0
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'?
 
  • #7
9
0
u' = e

?

:/
 
  • #8
1,291
0
u' = e

?

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

hint: e itself is equal to what?
 

Related Threads on Second Derivative of e^t + t^e ?

  • Last Post
Replies
2
Views
9K
Replies
5
Views
2K
Replies
4
Views
17K
  • Last Post
Replies
1
Views
980
  • Last Post
Replies
1
Views
1K
Replies
6
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
3
Views
9K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
1K
Top