If a function is even, prove that the derivative is odd.(adsbygoogle = window.adsbygoogle || []).push({});

Look at a graph of x^2 we can clearly see why.

This is how I would approach this...

If we solve d/dx x^n and n is an even integer, we get the derivative nx^(n-1). Since n is even, n-1 is odd.

Because n-1 is odd, the derivative nx^(n-1) becomes odd because f'(-x)= - f'(x). Therefore the derivative of an even function becomes an odd function.

Note: The TA couldn't solve this... :uhh:

I excluded the proof of d/dx x^n = nx^(n-1) because it is not necessary because I know how to do that.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Even and Odd functions

**Physics Forums | Science Articles, Homework Help, Discussion**