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

1 Answer
Aug 13, 2016

#f'(x)=(9x^2+6x-2)/(3x+1)^2#

Explanation:

differentiate using the #color(blue)"quotient rule"#

Given #f(x)=(g(x))/(h(x))" then "#

#color(red)(|bar(ul(color(white)(a/a)color(black)(f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2))color(white)(a/a)|))........ (A)#
#color(blue)"--------------------------------------------------------"#

#g(x)=3x^2+4x+2rArrg'(x)=6x+4#

#h(x)=3x+1rArrh'(x)=3#
#color(blue)"------------------------------------------------------"#
substitute these values back into (A)

#f'(x)=((3x+1)(6x+4)-(3x^2+4x+2).3)/(3x+1)^2#

#=(18x^2+18x+4-9x^2-12x-6)/(3x+1)^2#

#rArrf'(x)=(9x^2+6x-2)/(3x+1)^2#