How do you differentiate #f(x)= (2 x^2 - x - 6 )/ (x- 5 )# using the quotient rule?

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Answer 1 · 2017-01-17T07:08:00

The answer is #=(2x^2-20x+11)/(x-5)^2#

We need

#(x^n)'=nx^(n-1)#

We use the formula

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

Here,

#u=2x^2-x-6#, #=>#, #u'=4x-1#

#v=x-5#, #=>#, #v'=1#

Therefore,

#f'(x)=((4x-1)(x-5)-(2x^2-x-6)*1)/(x-5)^5#

#=(4x^2-21x+5-2x^2+x+6)/(x-5)^2#

#=(2x^2-20x+11)/(x-5)^2#