Let x=t^{2}+ t, and let y = sin t.

a. Find d/dt (dy/dx) as a function of t.

b. Find d/dx (dy/dx) as a function of t.

I understand how to do (a) part. Using the rule dy/dx = (dy/dt)/(dx/dt), I get dy/dx = (cos t) /(2t + 1). Using the Quotient Rule,

I get d/dt (dy/dx) = [-(2t +1)sin t - 2 cos t] / (2t +1)^{2}.

How do I find d/dx (dy/dx)? I think it would involve the Chain Rule but not sure where to start.