How e^-x got removed from the Numerator?

Thread Starter

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).

Some body please guide me.

Zulfi.

derivative of gradient slide.jpg
 

Thread Starter

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.
 
Top