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

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Answer 1 · 2016-05-31T04:56:01

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

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

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.

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