# Second Derivative of e^t + t^e ?

1. Nov 17, 2011

### catteyes

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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

2. Nov 17, 2011

### dacruick

you're quite close. after taking the first derivative, the exponent of t changes, you have not accounted for that.

3. Nov 17, 2011

### catteyes

I'm not sure I follow. Doesn't the exponent of t become (e-2) ?

4. Nov 17, 2011

### dacruick

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: Nov 17, 2011
5. Nov 17, 2011

### catteyes

scratch that... it didn't even look almost right

Last edited: Nov 17, 2011
6. Nov 17, 2011

### Nano-Passion

$$t^e$$
$$t^u = u' f'(u)$$

What is u'?

7. Nov 17, 2011

### catteyes

u' = e

?

:/

8. Nov 17, 2011

### Nano-Passion

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

hint: e itself is equal to what?