Differentiate with respect to time

Question

A turkey can run faster than it can fly backwards. Thus, it's position equation is represented by 2x+y=3. Differentiate with respect to time and find how fast it's changing when it's x is increasing at 1 meter per second.

Answer 1

This is an implicit differentiation problem

 

Differentiate wrt to t , d/dt(2x+y)=d/dt(3), 2x' + y' = 0 , y'=-2 x'

 

and x' is the rate of change of distance wrt to time x' = dx/dt,  1 m/sec , y' = dy/dt =  -2(1 m/sec) = -2 m/sec