Question

find the derivative of d^2x/dt^2
if x^3=at^2 thanks

Answer 1

x^3 = at^2
3x^2 x' = 2at
x' = 2at/3x^2
x" =
(2a)(3x^2) - (2at)(6xx')
-------------------------------
        9x^4

2ax - 4at(2at/3x^2)
-----------------------------
     3x^3

(6ax^3 - 8a^2t^2)/(9x^5)
= (6a^2t^2 - 8a^2t^2)/(9at^2 x^2)
= -2a / 9x^2

you can express that as a function of just t if you want.