Find the $ n $ th derivative of each function by calculating the first few derivatives and observing the pattern that occurs.
(a) $ f(x) = x" $ (b) $ f(x) = 1/x $
he It's clear. So in new Marine here. So we're gonna find the first few derivatives you have ever X is equal to X to the end power when we have our first derivative, which is X and times X to the n minus one power. We have our second derivative, which is n times and minus one X to the N minus two. And we see that, uh, to the then power derivative is equal to and times and minus one times and minus two all the way. Tow n minus and close one times X to the n minus. And and this becomes equal to in factorial For part B, we're gonna do the same thing. Just write a couple of derivatives to see the pattern. X Square becomes next for the second er, bit of negative one negative too. Next to the negative three years power. And then we have, uh, then derivative, which is equal to negative one times Negative too, comes negative three all the way to negative and times X to the negative and plus one power which is equal to negative one to the end. Power factorial over X to the end, plus one