How do you find the derivative of #y = (2x^4 - 3x) / (4x - 1)#?

1 Answer
May 31, 2016

Using the derivative rules we find that the answer is #(24x^4-8x^3+3)/(4x-1)^2#

Explanation:

Derivative rules we need to use here are:
a. Power rule
b. Constant Rule
c. Sum and difference rule
d. Quotient rule

  1. Label and derive the numerator and denominator
    #f(x)=2x^4-3x#
    #g(x)=4x-1#

By applying the Power rule, constant rule, and sum and difference rules, we can derive both of these functions easily:
#f^'(x)= 8x^3-3#
#g^'(x)=4#

at this point we will use the Quotient rule which is:
#[(f(x))/(g(x))]^'=(f^'(x)g(x)-f(x)g^'(x))/[g(x)]^2#

Plug in your items:
#((8x^3-3)(4x-1)-4(2x^4-3x))/(4x-1)^2#

From here you can simplify it to:
#(24x^4-8x^3+3)/(4x-1)^2#

Thus the derivitive is the simplified answer.