Question

How do you differentiate `f(x) =(2+x )( 2-3x)` using the product rule?

Answer 1

`-6x -4`

Explanation:

`f(x) = (2 + x)(2 - 3x)`

let say `u = (2 + x)`, then `u' = 1` and `v =(2 - 3x)`, then `v' = -3`

`f'(x) = uv' + vu'`

`f'(x) = (2 + x)(-3) +(2 - 3x)(1)`

`f'(x) = -6 -3x +2 - 3x = -6x -4`

Answer 2

-6x-4

Explanation:

If we want to differentiate `f(x)=(2+x)(2-3x)` using the product rule we use the following `(f')(g)+(g')(f)`. Where `f` is your first term `(2+x)` and `g` is your second term `(2-3x)`. So, we take the `d/dx` of `f` which is 1 using the power rule `nx^(n-1)` keep in mind that the `d/dx` of a constant is zero, while `g` remains the same. At this point what we have is `1(2-3x)` now we take the `d/dx` of `g` which is `-3`, `f` remains the same.

After we have derived the equation we now have the following:

`1(2-3x)-3(2+x)`

Go ahead distribute and simplify:

`2-3x-6-3x=-6x-4`

Our final answer is `-6x-4`.