I'm having problems using the quotient rule and am hoping that someone can help.

g(t) = A / 1+ BE^-t

Using the quotient rule the numerator simplifies to

0 - A(-BE^-t) = ABE^-t

I don't see how (1 + BE^-t)(A') simplifies to 0,

and how -A(1 + BE^-t)' simplifies to -A(-BE^-t).

In the latter if e is raised to the -t shouldn't that come down using the power rule and then it's e ^t-1?

Will someone please help?

Ted