My Math Forum How to differentiate square root with small number at the left and exponent inside?

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 May 1st, 2016, 03:14 PM #11 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 There are two things you need to know for that. Firstly, $(ab)^c = a^cb^c$. Secondly, $a^ba^c = a^{b + c}$. So for example, $\dfrac{1}{5}(7x^2)^{-4/5} = \dfrac{1}{5}\cdot7^{-4/5}x^{-8/5}$ Keep expanding like that and you should get the right hand side.
May 1st, 2016, 03:50 PM   #12
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 Originally Posted by Incomprehensible I'm not sure if this problem can be solved. I don't know the terminology for the math parts
Perhaps if you studied your precalculus notes, you would learn the correct terminology and what it means. The answer to your question would then be easy.

If you wish to understand a language, you must first understand how it is written.

 May 1st, 2016, 04:37 PM #13 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,823 Thanks: 643 Math Focus: Yet to find out.
 May 1st, 2016, 05:29 PM #14 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,663 Thanks: 2643 Math Focus: Mainly analysis and algebra I've put a reply into that thread, which I encourage the OP to read.
 May 4th, 2016, 12:33 PM #15 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 I want to add again my annoyance that the Latex code for "nth root" is "\sqrt[n]{x}"! This is titled "How to differentiate square root with a small number to the left" when, in fact, it has nothing to do with the a square root!

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