Question

How do you differentiate `f(x)= (x^2-5x+2)/ (x- 1 )` using the quotient rule?

Answer 1

`f'(x) = (x^2 - 2x + 3 )/(x - 1 )^2`

Explanation:

using the `color(blue) " Quotient Rule "`

`" If " f(x) = g(x)/(h(x)) rArr f'(x) = (h(x)g'(x) - g(x)h'(x))/[h(x) ]^2`

hence`f'(x) = ((x-1) d/dx(x^2-5x+2) - (x^2-5x+2) d/dx(x-1))/(x-1)^2`

`= ((x-1)(2x-5) - (x^2-5x+2).1)/(x-1)^2`

`= (2x^2-5x-2x+5 -x^2+5x - 2 )/(x-1)^2 = (x^2 -2x + 3 )/(x-1)^2`