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

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Answer 1 · 2014-10-10T21:03:04

First Derivative

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

Second Derivative

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

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