Question

How do you differentiate `f(x)=1/3(2x^3-4)` using the product rule?

Answer 1

`f'(x)=2x^2`

Explanation:

The product rule is not required here as there is not a product of 2 functions.

The `color(blue)"product rule"` is used in the following situation.

`f(x)=g(x).h(x)`

here `f(x)=2/3x^3-4/3" distribute the bracket"`

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

That is `color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(ax^n)=nax^(n-1)" and " d/dx("constant")=0)color(white)(a/a)|)))`

`rArrf'(x)=(3xx2/3)x^2-0=2x^2`