# How e^-x got removed from the Numerator?

#### zulfi100

Joined Jun 7, 2012
633
Hi
I am trying to understand a simple subtraction involving e^-x. Actually whole process is related to calculating partial derivative of sigmoid function. I got following from a lecture slide:
dy/dx= (1/(1+e^-x) ) * (e^-x + 1 -1)/(1 + e^-x)
I can't understand how can we remove e^-x from numerator as shown in the attached slide (i.e the last step).

Zulfi.

#### zulfi100

Joined Jun 7, 2012
633
Hi,
I am able to understand this. Numerator and denominator of 1st term within the brackets will divide each other producing 1.

Zulfi.

#### MrAl

Joined Jun 17, 2014
7,811
Hello,

The trick part is knowing in advance that e^-x+1-1 in the numerator will cause this '1' to appear later. because that e^-x+1 part is the same as 1+e^-x .
Sometimes these problems require looking in advance a little of what might happen if we change something a little, but sometimes it is hard to see.

#### WBahn

Joined Mar 31, 2012
26,148
Put the final result in square brackets over a common denominator.