Find the deriative dy/dx for y=x^2-2x/x^3+3

Question

asked Jan 10, 2021 233k views

1 Answer

Rachael · Answer 1 · 2021-01-14T14:10:30+0000

Answer:

(dy)/(dx)=(((2x-2)(x^3+3)-(x^2-2x)(3x^2))/((x^3+3)^2))

Explanation:

So we want to find the derivative of the rational equation:

y=(x^2-2x)/(x^3+3)

First, recall the quotient rule:

((f)/(g))'=(f'g-fg')/(g^2)

Let f be x^2-2x and let g be x^3+3.

Calculate the derivatives of each:

$f=x^2-2x\\f'=2x-2$

$g=x^3+3\\g=3x^2$

So:

(dy)/(dx)=((x^2-2x)/(x^3+3))'

Use the above format:

$(dy)/(dx)=(f'g-fg')/(g^2)\\(dy)/(dx)=(((2x-2)(x^3+3)-(x^2-2x)(3x^2))/((x^3+3)^2))$

And that's our answer :)

(If you want to, you can also expand. However, no terms will be canceled.)