Question

can someone teach me how to obtain the nth derivative of the following function

Answer 1

write down the first few derivatives and then spot the pattern

Answer 2

ok

Answer 3

\[f(x)=\frac{2}{x+1}=2(x+1)^{-1}\]\[f'(x)=-2(x+1)^{-2}\]

Answer 4

\[f''(x)=4(x+1)^{-3}\]\[f'''(x)=-12(x+1)^{-4}\]

Answer 5

emunrradtvamg: can you see the pattern?

Answer 6

I got it. Thank you very much guys

Answer 7

yeah I can se the patter now. I already had the answer. but I was wondering how to get to it

Answer 8

ok - great!

Answer 9

what is the answer?
\[f^{n}(x)=\cdots\]

Answer 10

this is the answer

Answer 11

the pattern I can see is:\[f^n(x)=\frac{(-1)^n\times2\times n!}{(x+1)^{n+1}}\]

Answer 12

emunrradtvamg: is your images /chopped/? it seems to be missing the factorial sign

Answer 13

let me check it out

Answer 14

yeah you are right

Answer 15

thanks again

Answer 16

yw