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# Advanced Math/Chain rule with f(x) and g(x)

Question
Hi Clyde

I don't really know how to find the derivative of a function like
[f(x)]^2/[g(2x)+2x] and need some help on it.

Sam

To solve problems like this, you apply the usual rules for differentiation:

Quotient rule: (u/v)' = (u'v - uv')/v^2

Here, u=f(x)^2, so u' = 2f(x)f'(x) by the power & chain rules.

Similarly, v=g(2x)+2x, which is 2g'(2x)+2 by the chain rule.

[ 2f(x)f'(x)(g(2x)+2x) - f(x)^2 (2g'(2x)+2) ] / [ (2g'(2x)+2)^2 ]

Volunteer

#### Clyde Oliver

##### Expertise

I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks.

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I am a PhD educated mathematician working in research at a major university.

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Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

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BA mathematics & physics, PhD mathematics from a top 20 US school.

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Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

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In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.