Question

How do you differentiate `g(t)=t^3cost`?

Answer 1

`g'(t)=3t^2cost-t^3sint`

Explanation:

We will differentiate `g(t)` using the product rule:
`[ab]'=a'b+b'a`, letting `a=t^3` and `b=cost`.
`a'=3t^2` and `b'=-sint`. Substituting `a` and `b` into the product rule, we get `[t^3cost]'=3t^2cost-t^3sint`, or `g'(t)=3t^2cost-t^3sint`.

Answer 2

`g'(t)=3t^2cost-t^3sint`

Explanation:

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

`"given "g(t)=f(t)h(t)" then"`

`g'(t)=f(t)h'(t)+h(t)f'(t)larrcolor(blue)"product rule"`

`f(t)=t^3rArrf'(t)=3t^2`

`h(t)=costrArrh'(t)=-sint`

`g'(t)=-t^3sint+3t^2cost`