Question

What is the derivative of `t^2*2^t`?

Answer 1

`t^2 2^tln2+2t.2^t`

Explanation:

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

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

`dy/dt=f(t)g'(t)+g(t)f'(t)larrcolor(blue)"product rule"`

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

`g(t)=2^trArrg'(t)=2^t ln2`

`rArrd/dt(t^2 .2^t)`

`=t^2 2^tln2+2t.2^t`