Question

How do you differentiate `s=(t^-1+t^-2)/t^-3`?

Answer 1

`s'(t)=2t+1`

Explanation:

First rewrite the function:

`s(t)=(1/t+1/t^2)/(1/t^3)=t^3(1/t+1/t^2)=t^2+t`

Through the product rule, which states that `d/dt(t^n)=nt^(n-1)`, we see that:

`s'(t)=2t^(2-1)+1t^(1-1)=2t^1+1t^0=2t+1`