How do you derive #y = (4x − 2) / (x^2 + 1)# using the quotient rule?

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Answer 1 · 2016-01-06T19:07:08

For "How", see the explanation section, below.

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

In this function, we have #u=4x-2# so #u'=4#

and #v=x^2+1#, so #v'=2x#.

Apply the rule:

#f'(x) = ([4][x^2-1]-[4x-2][2x])/(x^1-1)^2#

# = (4x^2-4-8x^2+4x)/(x^2-1)^2#

# = (-4x^2+4x-4)/(x^2-1)^2#.

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