Question

If f(x) is an even function, then f '(x) is (even or odd?)
If g(x) is an odd function, then g ' (x) is (even or odd?)

I am unsure of how to approach this question.

Answer 1

Well ...a function is even...if it has an even exponent right...a function is odd if it has an odd exponent...so

think of the power rule...

when you take the derivative of 3x² (even function) you get 6x (odd function)

when you take the derivative of 3x^3 (odd function) you get 9x² (even function)

Answer 2

Oh, I see. I wasn't sure if I could just approach it in that manner.
So then f '(x) would be odd and g '(x) would be even.

Answer 3

Thank you!

Answer 4

anytime!