Let f(x)={x^n(1-x)^n}/n!. Then for any integer k>0, the kth derivatives f^(k)(0) and f^(k)(1)
A. are both 0 B. are both rational numbers but not necessarily integers
C. are both integers D. do not satisfy any of the foregoing properties

i was getting A as the answer but that is not right..

How did you arrive at your answer? What were your steps and reasoning?

Please be complete. Thank you!

I just differentiated the function once and than twice and had put x=0, 1. The method I employed was more like a hit and trial method. It would be great if you could give a more systematic approach to the question.

You could try finding more than just the first two derivatives... (Patterns sometimes take a while to "see".)

i did, but i was getting 0 only as the answer. Kindly help!