If a function is even, prove that the derivative is odd. 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.