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March 2, 2015

March 2, 2015

Posted by **Angie** on Saturday, September 22, 2012 at 10:45am.

Differentiate the following using the chain rule.

f(x) = squareroot(x^2+1)/(3x+1)

I know that I can take the whole thing and put it to the (1/2) and differentiate that then use the quotient rule to differentiate the inside, but when i try to factor I can't get stuck. with 3x^2+2x-3/(3x+1)^2

- Calculus -
**Steve**, Saturday, September 22, 2012 at 3:43pmassuming you mean

f(x) = √((x^2+1)/(3x+1))

f = u^1/2 where u = (x^2+1)/(3x+1)

so,

f' = 1/2√u u'

u = f/g where

f = x^2+1 and v = 3x+1

so, u' = (f'g-g'f)/g^2 = (3x^2+2x-3)/(3x+1)^2

so f' = 1/[2√((x^2+1)/(3x+1))] * (3x^2+2x-3)/(3x+1)^2

= (3x^2+2x-3)/[2(3x+1)^{3/2}(x^2+1)^{1/2}]

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