How do you differentiate #f(x) = (x)/(x^2-x+6)# using the quotient rule?

1 Answer
Jim G.
Apr 15, 2016

# (6 - x^2)/(x^2 - x + 6)^2 #

Explanation:

differentiate using the #color(blue)" quotient rule " #

If f(x) =#(g(x))/(h(x))" then " f'(x) = (h(x).g'(x) - g(x).h'(x))/(h(x))^2 #
#"---------------------------------------------------------------------"#

g(x) = x #rArr g'(x) = 1 #

and h(x) #= x^2 - x + 6 rArr h'(x) = 2x - 1 #
#"------------------------------------------------------------------"#
substitute these values into f'(x)

#rArr f'(x) =( (x^2-x+6).1 - x(2x-1))/(x^2-x+6)^2 #

#=(x^2-x+6 -2x^2+ x)/(x^2-x+6)^2 = (6-x^2)/(x^2-x+6)^2 #

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