How do you differentiate #f(x)= (6 x^2 - x - 6 )/ (x- 1 )# using the quotient rule?
1 Answer
Jul 4, 2017
Explanation:
#"given " f(x)=(g(x))/(h(x))" then"#
#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#
#g(x)=6x^2-x-6rArrg'(x)=12x-1#
#h(x)=x-1rArrh'(x)=1#
#rArrf'(x)=((x-1)(12x-1)-(6x^2-x-6).1)/(x-1)^2#
#color(white)(rArrf'(x))=(12x^2-13x+1-6x^2+x+6)/(x-1)^2#
#color(white)(rArrf'(x))=(6x^2-12x+7)/(x-1)^2#
