How do you differentiate #f(x)= x/(x-3 )# using the quotient rule?

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Answer 1 · 2017-03-02T11:37:46

#f'(x) = -3/(x-3)^2#

If #f(x) = g(x)/(h(x))# then the quotient rule states that:

#f'(x) = (h(x) * g'(x) - g(x) * h'(x))/ [h(x)]^2#

In this example: # f(x) = x/(x-3)#

Hence: #g(x) = x# and #h(x) = (x-3)#

Applying the quotient in this example:

#f'(x) = ((x-3)*1 - x*1) / (x-3)^2#

#= (x-3-x)/(x-3)^2#

#= -3/(x-3)^2#