Second Derivative of a Polar Coordinate

Question

https://snag.gy/buiJve.jpg

I'm not sure what the issue is, but I've calculated this several times and have been unable to produce the correct answer. I have followed the procedures.

I went to calculate the second Derivative using the equation

    d/dt(dy/dx)/(dx/dt)

Answer 1

As you did, the first derivative is found by

$$y'(t)=\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}},$$

where the "$'$" is derivative with respect to x.

Same thing for the second derivative:

$$y''(t)=\frac{dy'}{dx} = \frac{\frac{dy'}{dt}}{\frac{dx}{dt}}.$$

I get

$$\frac{2t}{(t+1)^3}$$