How do you differentiate #f(x)= (4 x^2 + 2x -3 )/ (x- 1 )# using the quotient rule?

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Answer 1 · 2018-03-07T13:20:18

#f'(x) = (4x^2 -8x +1)/(x-1)^2#

#f(x) = color(red)(u) /color(blue)(v)#

#f'(x) = (color(blue)(v) color(red)(u') - color(blue)(v') color(red)(u))/ color(blue)(v^2)#

Hence, to differentiate the given #f(x)#, you do the following

#f'(x)= ((color(blue)(x-1)) (color(red)(8x+2)) - (color(blue)(1)) (color(red)(4x^2 + 2x -3)))/(color(blue)((x-1)^2))#

#f'(x) = (8x^2 + 2x - 8x - 2 - 4x^2-2x+3)/(x-1)^2#

#f'(x) = (4x^2 -8x +1)/(x-1)^2#

There is no need to simplify any further after this point