# What is the instantaneous velocity of an object moving in accordance to # f(t)= (t-e^t,te^(2t)) # at # t=3 #?

##### 1 Answer

Instantaneous velocity is

or in vector form

or

#### Explanation:

I assume that f(t) is a position, Standard convention for a position in space would be

Then we can get the velocity by differentiaiting (we will need to use the product rule and chain rules) as

Differentiating wrt

When

Hence the instantaneous velocity is

or in vector form

or