Tuesday, September 2, 2014

Differentiate the function y=(3x^2-2)/(3x^2+2)

We notice that we'll have to determine the derivative of a
fraction, so, we'll have to use the quotient rule.


(u/v)' =
(u'*v - u*v')/v^2


We'll put u = 3x^2-2 => u' =
6x


We'll put v =3x^2+2=> v' =
6x


We'll substitute u,v,u',v' in the formula
above:


f'(x) = [6x*(3x^2+2) -
(3x^2-2)*6x]/(3x^2+2)^2


We'll factorize by
6x:


f'(x) = 6x(3x^2+2 - 3x^2 +
2)/(3x^2+2)^2


We'll combine and eliminate like terms inside
brackets:


f'(x) = 6x
*(4)/(3x^2+2)^2


f'(x) =
24x/(3x^2+2)^2

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