How do you differentiate #f(x)= (x+2)/ (x- 7 )# using the quotient rule?

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Answer 1 · 2018-03-26T22:48:14

#f'(x)=-9/(x-7)^2#

The quotient rule tells us if:

#f(x) = u/v#

then:

#f'(x) = (u'v-uv')/v^2#

In our case:

#u = x+2 implies u' =1#

and:

#v = x-7 implies v'=1#

So:

#f'(x) = (1*(x-7)-(x+2)*1)/(x-7)^2#

Simplifying:

#f'(x)=-9/(x-7)^2#