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4:59

The second derivative of a single valued function parametrically represented by `x=varphi(t)a n dy=psi(t)` (where `varphi(t)a n dpsi(t)` are different function and `varphi^(prime)(t)!=0` ) is given by `(d^2y)/(dx^2)=(((dx)/(dt))((d^2y)/(dt^2))-((d^2x)/(dt^2))((dy)/(dt))/(((dx)/(dt))^2)` `(d^2y)/(dx^2)=(((dx)/(dt))((d^2y)/(dt^2))-((d^2x)/(dt^2))((dy)/(dt))/(((dx)/(dt))^3)` `(d^2y)/(dx^2)=(((d^2x)/(dt))((d^y)/(dt^2))-((d^x)/(dt^))((d^2y)/(dt^2))/(((dx)/(dt))^3)` `(d^2y)/(dx^2)=(((d^2x)/(dt^2))((d^y)/(dt^))-((d^2x)/(dt^2))((d^y)/(dt^))/(((dx)/(dt))^3)`

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1:44

The second derivative of a single valued function parametrically represented by `x=varphi(t)a n dy=psi(t)` (where `varphi(t)a n dpsi(t)` are different function and `varphi^(prime)(t)!=0` ) is given by `(d^2y)/(dx^2)=(((dx)/(dt))((d^2y)/(dt^2))-((d^2x)/(dt^2))((dy)/(dt))/(((dx)/(dt))^2)` `(d^2y)/(dx^2)=(((dx)/(dt))((d^2y)/(dt^2))-((d^2x)/(dt^2))((dy)/(dt))/(((dx)/(dt))^3)` `(d^2y)/(dx^2)=(((d^2x)/(dt))((d^y)/(dt^2))-((d^x)/(dt^))((d^2y)/(dt^2))/(((dx)/(dt))^3)` `(d^2y)/(dx^2)=(((d^2x)/(dt^2))((d^y)/(dt^))-((d^2x)/(dt^2))((d^y)/(dt^))/(((dx)/(dt))^3)`

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