D (x) = (x + 1) (x + 2) ^ 2 (x +3) ^ 3 (x + 4) ^ 4 (x + 5)

Find the derivative at -1

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- Dec 20th 2009, 09:47 AMdaporeVery cool
**D (x) = (x + 1) (x + 2) ^ 2 (x +3) ^ 3 (x + 4) ^ 4 (x + 5)**

Find the derivative at -1 - Dec 20th 2009, 09:51 AMe^(i*pi)
- Dec 20th 2009, 10:04 AMskeeter
- Dec 20th 2009, 11:23 AMJester
You could go right to the definition

as Skeeter said. - Dec 20th 2009, 12:18 PMoblixps
I'm curious, why didn't logarithmic differentiation work for this problem?

- Dec 20th 2009, 12:20 PMVonNemo19
- Dec 20th 2009, 12:53 PMskeeter
- Dec 20th 2009, 04:18 PMoblixps
but ln(1+e^(i*pi)) = ln(0), doesn't the limit not exist?

- Dec 20th 2009, 05:21 PMoblixps
after differentiating both sides and multiplying both sides by , you'll get y'=

then distribute and plug in x = -1 and you'll see that all the terms will cancel out and become zero except for the first term, since the (x+1)s cancel out. when you plug in x = -1 to what you have left, you'll get - Dec 21st 2009, 08:25 AMdapore
**You the most beautiful tribute (Clapping)**

- Dec 21st 2009, 09:16 AMKrahl
- Dec 21st 2009, 11:32 AMoblixps
e^(i*pi) said the derivative does not exist because of the 1/(x+1) term but in fact it just cancels out when you distribute so the derivative does exist. I was just correcting a small mistake.