How can I find the general term for this derivative?
I want to find the general term for the nth derivative of (where x=0):
$frac{x^2}{left(x-1right)^2}$ , $x=0$
Wolfram alpha gives me the direct answer:
$frac{d^n}{dx^n}$$left(frac{x^2}{left(x-1right)^2}right) = (n-1)n!$$,nge1$
How do I get to this answer?
calculus
asked Nov 24 at 23:57
Pedro Capelas
11
add a comment |
I want to find the general term for the nth derivative of (where x=0):
$frac{x^2}{left(x-1right)^2}$ , $x=0$
Wolfram alpha gives me the direct answer:
$frac{d^n}{dx^n}$$left(frac{x^2}{left(x-1right)^2}right) = (n-1)n!$$,nge1$
How do I get to this answer?
calculus
asked Nov 24 at 23:57
Pedro Capelas
11
add a comment |
I want to find the general term for the nth derivative of (where x=0):
$frac{x^2}{left(x-1right)^2}$ , $x=0$
Wolfram alpha gives me the direct answer:
$frac{d^n}{dx^n}$$left(frac{x^2}{left(x-1right)^2}right) = (n-1)n!$$,nge1$
How do I get to this answer?
calculus
asked Nov 24 at 23:57
Pedro Capelas
11
I want to find the general term for the nth derivative of (where x=0):
$frac{x^2}{left(x-1right)^2}$ , $x=0$
Wolfram alpha gives me the direct answer:
$frac{d^n}{dx^n}$$left(frac{x^2}{left(x-1right)^2}right) = (n-1)n!$$,nge1$
How do I get to this answer?
calculus
calculus
asked Nov 24 at 23:57
Pedro Capelas
11
asked Nov 24 at 23:57
Pedro Capelas
11
edited Nov 25 at 0:00
asked Nov 24 at 23:57
Pedro Capelas
11
asked Nov 24 at 23:57
Pedro Capelas
11
asked Nov 24 at 23:57
Pedro Capelas
11
11
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
Hint: Note that
begin{align}
frac{x^2}{(1-x)^2} = x^2 frac{d}{dx}left(frac{1}{1-x}right)
end{align}
then Taylor expand.
answered Nov 25 at 0:01
Jacky Chong
17.6k21128
add a comment |
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Hint: Note that
begin{align}
frac{x^2}{(1-x)^2} = x^2 frac{d}{dx}left(frac{1}{1-x}right)
end{align}
then Taylor expand.
answered Nov 25 at 0:01
Jacky Chong
17.6k21128
add a comment |
Hint: Note that
begin{align}
frac{x^2}{(1-x)^2} = x^2 frac{d}{dx}left(frac{1}{1-x}right)
end{align}
then Taylor expand.
answered Nov 25 at 0:01
Jacky Chong
17.6k21128
add a comment |
Hint: Note that
begin{align}
frac{x^2}{(1-x)^2} = x^2 frac{d}{dx}left(frac{1}{1-x}right)
end{align}
then Taylor expand.
answered Nov 25 at 0:01
Jacky Chong
17.6k21128
Hint: Note that
begin{align}
frac{x^2}{(1-x)^2} = x^2 frac{d}{dx}left(frac{1}{1-x}right)
end{align}
then Taylor expand.
answered Nov 25 at 0:01
Jacky Chong
17.6k21128
answered Nov 25 at 0:01
Jacky Chong
17.6k21128
answered Nov 25 at 0:01
Jacky Chong
17.6k21128
answered Nov 25 at 0:01
Jacky Chong
17.6k21128
17.6k21128
add a comment |
add a comment |
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