Product Rule

Question

Have been learning about product rule and stuck on this question:

 

The displacement, y(m), of a body in damped oscillation is y = 2e^-tsin3t

 

• Use the product rule to find an equation for the velocity of the object if v = dy/dt

Answer 1

y(t) = 2e^-tsin3t

 

Use the product rule AND the chain rule.

 

v = dy/dt = 2(-e^-tsin3t + 3e^-tcos3t)

 

You can simplify it further if you wish, or even get it in the form

 

y(t) = Ae^-tsin(3t + B) = A'e^-tcos(3t + B')