Asked by Anonymous
Find the nth derivative of y=2x/(1-x^2)
(Hint: Consider -[(1/(x-1))+(1/(x+1))].)
(Hint: Consider -[(1/(x-1))+(1/(x+1))].)
Answers
Answered by
Steve
so, did you even think about the hint?
2x/(1-x^2) = 2x/((1-x)(1+x)
= -[1/(x+1) + 1/(x-1)]
The nth derivative of 1/(x+1) and 1/(x-1) is easy to figure, right?
2x/(1-x^2) = 2x/((1-x)(1+x)
= -[1/(x+1) + 1/(x-1)]
The nth derivative of 1/(x+1) and 1/(x-1) is easy to figure, right?
Answered by
Anonymous
Or how do I find the formula for this?
Answered by
Steve
huh? Let's take f=1/u. (Let u=x+1 or u=x-1)
<sup></sup>
f = 1/u = u^<sup>-1</sup>
f' = -1 u<sup>-2</sup>
f" = (-1)(-2)u<sup>-3</sup>
...
f<sup>n</sup> = (-1)<sup>n</sup>n! u<sup>-(n+1)</sup>
<sup></sup>
f = 1/u = u^<sup>-1</sup>
f' = -1 u<sup>-2</sup>
f" = (-1)(-2)u<sup>-3</sup>
...
f<sup>n</sup> = (-1)<sup>n</sup>n! u<sup>-(n+1)</sup>
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