How do you differentiate #f(x) = (5x)/(3x^2-x+1)# using the quotient rule?
1 Answer
Jul 22, 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)=5xrArrg'(x)=5#
#h(x)=3x^2-x+1rArrh'(x)=6x-1#
#rArrf'(x)=((3x^2-x+1).5-5x(6x-1))/(3x^2-x+1)^2#
#color(white)(rArrf'(x))=(15x^2-5x+5-30x^2+5x)/(3x^2-x+1)^2#
#color(white)(rArrf'(x))=(5-15x^2)/(3x^2-x+1)^2#
