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I'm having problems with this one. Can't get the right answer.

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 -

    assuming you mean

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