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LeoMessi
How do I use the quotient rule on this function: (4x − 2) / (x2 + 1) ?
\[ \frac{4x-2}{x^{2}+1} \]
\[f(x) = \frac{g(x)}{h(x)} => \frac{h'(x) * g(x) - g'(x)*h(x)}{[h(x)]^2} \]
\[f(x) = \frac{Top Func.}{Bottom Func} => \frac{Deriv. of Bottom Func * Top func. - Deriv. of Top func. * Bottom Func}{[Bottom Func]^2} \]
so here: g(x) = 4x-2, h(x) = x^2 + 1
OH, cool, I'll give it a shot: g(x) = (4x-2), h(x) = x^2+1. g'(x) = 4, h'(x) = 2x
so: \[\frac{2x * (4x-2) - 4*(x^2+1)}{[(x^2+1)]^2} \]
you can try to simplify here too
d/dx= ((2x)(4x-2)-(4)(x^2+1))/ (x^2+1)^2 =4x^2-4x-4/ (x^2+1)^2
Go here http://www.wolframalpha.com/input/?i=integrate+%284x%E2%88%922%29%2F%28x^2%2B1%29 and click "show steps"
4/(x^2+1)-(2*(4*x-1))*x/(x^2+1)^2