On the derivative of recursive functions

After I finished high school, I found an interesting math identity. I don’t know if this result is known, but here it is.

If we consider a bijective function, we can compose the function with itself, leading to recursive functions. We can derive a composed function by applying the chain rule.

Let’s define a recursive function f as a bijective function g composed on itself n times. If we take the derivative of the function f, we get the derivative of g to the power n.

The demonstration can be made using induction.

 

Advertisements
This entry was posted in Electronics and tagged , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s