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

1 Answer
Feb 15, 2016

Answer:

#h'(x) = (color(red)(6x)color(green)((3x+1)) - color(blue)(3)(3x^2-4))/(color(green)((3x+1)^2) #

Explanation:

Given:
#Let h(x) = f(x)/g(h) #
Quotient Rule says:
#h'(x) = (g(x)f'(x) - g'(x)f(x))/[g(x)]^2#
Now in your case set:
1) #f(x) = 3x^2-4; " then " f'(x) = color(red)(6x) #
2) #g(x) = color(green)(3x+1); " and " g'(x) = color(blue)3#

Solution is:
#h'(x) = (color(red)(6x)color(green)((3x+1)) - color(blue)(3)(3x^2-4))/(color(green)((3x+1)^2) #

Note I used: #h'(x) = (dh(x))/(dx)#
Cheers!