Second derivative of parametric equation

Question

Hi! I need help with the following problem:

A particle moves in a plane according to the parametric equations x(t) = 1 + 3cost, y(t) = 3sin2t. Find  in terms of t.

Answer choices:

    

I got an answer; however, I am unsure how to simplify it to get one of the answer choices. Please help. Thank you!

Answer 1

solve for dy/dx = dy/dt / dx/dt = 6cos(t)/(-3sint) = -2cos2t/sint

Now solve for d/dx(dy/dx) = d/dt(dy/dx)/ dx/dt = ((sin(t)(4sin(2t))-(-2cos(2t)(cos(t))/(-3sin³(t))

which is the 4th choice.

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