Question

What is the derivative of `f(x) = (x^3-3)/x`?

Answer 1

The derivative of `f(x)` is `(2x^3+3)/(x^2)`.

Explanation:

Using the quotient rule of derivatives:

`d/dx((f(x))/(g(x)))=(d/dx(f(x))*g(x)-f(x)*d/dx(g(x)))/((g(x))^2)`

Here's our expression:

`color(white)=d/dx((x^3-3)/x)`

`=(d/dx(x^3-3)*x-(x^3-3)*d/dx(x))/(x^2)`

`=((3x^2-0)*x-(x^3-3)*1)/(x^2)`

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

`=(2x^3+3)/(x^2)`

This is the derivative. Hope this helped!