If y = (sin t)^5t , find dy/dx.

Question

If y = (sin t)^5t , find dy/dx. (Hint: This is not the power rule.)

Answer 1

It's not the power rule, but the product rule we use here. 

 

y = sint*5t

y = U * V
First of all we can't find dy/dx because there is no x term. If we were to find dy/dx, we would have to treat all other variables as a constant which makes the dy/dx for this particular question = 0. 

Instead, I am going to assume we need dy/dt.

 

dy/dt = U*dV/dt + V*dU/dt

dy/dt = sint*5    + 5t*cost       

 

dy/dt = 5sin(t) +5tcos(t)