My Math Forum Chain rule on square root, what do you do with the number in the V?

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 November 6th, 2015, 07:41 AM #1 Newbie   Joined: Jan 2015 From: Philadelphia Posts: 20 Thanks: 2 Chain rule on square root, what do you do with the number in the V? So let's say the problem is f(x)=square root (with the 3 within the v part of the square root) of (1-x)^2. I know with square roots we just put 1/2 as the exponent, but I don't know what to do with that 3 that's within the v.
 November 6th, 2015, 07:44 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms $\sqrt[3]x$ is the cube root, not the square root. In general $\sqrt[n]x=x^{1/n}$ so you would use 1/3 instead of 1/2. Thanks from topsquark
 November 6th, 2015, 02:22 PM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 It really irks me that the Latex formula for a cube root, $\displaystyle \sqrt[3]{x}$, is "\sqrt[3]{x}", in other words, using "sqrt" for a cube root!
November 7th, 2015, 05:27 PM   #4
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Quote:
 Originally Posted by Country Boy It really irks me that the Latex formula for a cube root, $\displaystyle \sqrt[3]{x}$, is "\sqrt[3]{x}", in other words, using "sqrt" for a cube root!
Yes, I had the same thought as I typed out my answer!

November 7th, 2015, 06:22 PM   #5
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Quote:
 Originally Posted by CRGreathouse Yes, I had the same thought as I typed out my answer!
You could do what I always do: $\displaystyle x^{1/3}$. I simply don't mess with the sqrt[3]{x} thing.

-Dan

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