Question

How do you differentiate `V(x)=(2x^3+3)(x^4-2x)`?

Answer 1

`V'(x)=14x^6-4x^3-6`

Explanation:

Using the product rule

`(fg)'=f'g+fg'`
we get
`V'(x)=6x^2(x^4-2x)+(2x^3+3)(4x^3-2)`

Expanding we get

`V'(x)=6x^6-12x^3+8x^6+12x^3-4x^3-6`

`V'(x)=14x^6-4x^3-6`

Answer 2

`V'(x)=14x^6-4x^3-6`

Explanation:

`"differentiate using the "color(blue)"power rule"`

`•color(white)(x)d/dx(ax^n)=nax^(n-1)`

`"expand the factors using FOIL"`

`V(x)=2x^7-4x^4+3x^4-6x`

`color(white)(V(x))=2x^7-x^4-6x`

`V'(x)=14x^6-4x^3-6`