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.

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# Even and Odd functions

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