Question

Differentiate `y=x^3-4/(2x)+3`?

Answer 1

Assuming you are asking for `y=x^3-4/(2x)+3`
Then the derivative is `y'=3x^2+2/x^2`

Explanation:

`y=x^3-4/(2x)+3`
`y' = 3x^2-d/dx(2/x)+0`
`y'=3x^2-2*(-x^-2)`
`y'=3x^2+2/x^2`

Answer 2

`y'=3x^2+2x^-2`

Explanation:

We know we're dealing with a polynomial here, so to find the derivative, we can use the Power Rule, where the coefficient comes out front, and the exponent gets decremented by one.

First, I can rewrite our polynomial as

`y=x^3-color(blue)(2x^-1)+3`

NOTE: I rewrote `4/(2x)` by dividing the top and bottom by `2`, and bringing the `x` out of the denominator.

Now we just use the Power Rule a bunch. We get

`y'=3x^2+2x^-2`

Which can be alternatively written as

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

Hope this helps!