How do you differentiate #f(x)=(2x^2-4x-1)/(x-5)# using the quotient rule?

1 Answer
Sonnhard
May 25, 2018

#f'(x)=(2x^2-16x+1)/(x-5)^2#

Explanation:

Using the Quotient rule #(u'v-uv')/v^2# we obtain with
#u=2x^2-4x-1# then #u'=4x-4#
and #v'=1#
then
#f'(x)=(4x(x-5)-(2x^2-4x-1)*1)/(x-5)^2#
Simplifying
#f'(x)=(4x^2-20x-2x^2+4x+1)/(x-5)^2#
#f'(x)=(2x^2-16x+1)/(x-5)^2#

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