Question

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

Answer 1

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.