Why is d²x/dt² wrong for x+e^x=t?

[coverband]

Homework Statement

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

Homework Equations

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?

 

[LCKurtz]

Homework Statement

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

Homework Equations

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?

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.

 

[annoymage]

yea, its not 0

how do you differentiate

(1+e^x)^-1 ??

 

[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.