Question

How do you find `(d^2y)/(dx^2)` for the curve `x=4+t^2`, `y=t^2+t^3` ?

Answer 1

First Derivative

`{dy}/{dx}={{dy}/{dt}}/{{dx}/{dt}}={y'(t)}/{x'(t)}={2t+3t^2}/{2t}=1+3/2t`

Second Derivative

`{d^2y}/{dx^2}=d/{dx}{dy}/{dx}={d/{dt}{dy}/{dx}}/{{dx}/{dt}}={d/{dt}(1+3/2t)}/{x'(t)}={3/2}/{2t}=3/{4t}`

I hope that this was helpful.