Question

How do you differentiate `g(t)=(2/t+t^5)(t^3+1)` using the product rule?

Answer 1

`g'(t) = (-2t^-2 +5t^4)(t^3+1) + (2t^-1 +t^5)*3t^2`

Explanation:

The product rule says if:
`f(x) = u(x)*v(x)`
then
`f'(x) = u'(x)*v(x) + u(x)*v'(x)`

In your equation `g(t)`
Let
`u(t) = 2t^-1 + t^5` then `u'(t) = -2t^-2 + 5t^4`
and
`v(t) = t^3+1` then `v'(t) = 3t^2`

So
`g'(t) = u'(x)*v(x) + u(x)*v'(x)`

`g'(t) = (-2t^-2 +5t^4)(t^3+1) + (2t^-1 +t^5)*3t^2`