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find g'(t) if g(t) = te(e-1) [it reads t to the exponent of e times e to the exponent -1
Was thinking that e is a constant so the power rule might apply and would end up with -e(ln(te-1)).

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Questioner:JJ
Country:Colorado, United States
Category:Calculus
Private:No
Subject:Power rule

Question:
find g'(t) if g(t) = te(e-1) [it reads t to the exponent of e times e to the exponent -1
Was thinking that e is a constant so the power rule might apply and would end up with -e(ln(te-1)).
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If you mean:

g(t) = t^e e^-1,

that is
       t^e
g(t) = -----
        e

Now the 'e' on top is an exponent for base t, the variable, so yes, the power rule would apply.
But the 'e' on the bottom is simply a constant coefficient.

So you should get:

       e t^(e-1)
g'(t) = ---------
        e

= t^(e-1)  or t^e/t, if you like.

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