Find ds/dt for set of equations

Question

Find ds/dt for s = 2ln(v) and v = e^t/t

Answer 1

You want to take the derivative of v in terms of t.  You have to write function s in term of t in order to do the derivative.

 

Substitute v=e^tt into function s.

 

s = 2ln(e^t/t)

 

Then, use properties of logs.

 

s = 2tlne - 2lnt

 

s = 2t - 2lnt

 

 

Now you can take the derivative.