For i seem to get different answers, depending on the method.
1.
2. If i factor out the e term.
One of these is more correct than the other, which is it?
You are mixing the x and t when calculating the derivative.
If the power of "e" is -2t, then you have a product of 2 functions of "t".
If you differentiate with respect to x, you do not know what the derivative of "t" is, if t is itself a function of x.
For i seem to get different answers, depending on the method.
1.
2. If i factor out the e term.
One of these is more correct than the other, which is it?
The mistake you are doing, is that you are differentiating with respect to t sometimes and x the others. means you are differentiating with respect to x, so, . What you didn't notice is that
Hope that helps