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Question
Find `bb((d^2y)/(dx^2))` of the following:
x = 2at2, y = 4at
Solution
x = 2at2, y = 4at
Differentiating x and y w.r.t. t, we get
`dx/dt = d/dt(2at^2)`
= `2a*d/dt(t^2)`
= 2a × 2t
= 4at ...(1)
and `dy/dt = d/dt(4at)`
= `4a d/dt(t)`
= 4a × 1
= 4a
∴ `dy/dx = ((dy/dt))/((dx/dt)`
= `(4a)/(4at)`
= `1/t`
and `(d^2y)/(dx^2) = d/dx(1/t)`
= `d/dt(t^-1) xx dt/dx`
= `-1(t)^-2 xx 1/((dx/dt)`
= `-1/t^2 xx 1/(4at)` ...[By (1)]
= `-1/(4at^3)`
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