Homework Help: Implicit diff?

1. Apr 16, 2010

coverband

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

x+e^x=t. find dx/dt and d^2x/dt^2

2. Relevant equations

3. The attempt at a solution
dt/dx = 1 + e^x
Therefore dx/dt = (1+e^x)^-1 This is right.
d^2x/dt^2 = 0. This is wrong. Why?

2. Apr 16, 2010

LCKurtz

Because x is a funtion of t, not constant. You need to use the chain rule. And it would also have been more in the spirit of the problem to differentiate the original equation implicitly instead of solving for t.

3. Apr 16, 2010

annoymage

yea, its not 0

how do you differentiate

(1+ex)-1 ??

4. Apr 16, 2010

irycio

Well, given that x=x(t) (x being a function of t) you get $$-(1+e^x)^{-2}*e^x*\frac{dx}{dt}$$ And you've already calculated dx/dt.