find `(d^2y)/(dx^2)` of `2x^2-7y^2=21` by using implicit differentiation

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Given `2x^2-7y^2=21`

For the first derivative, using chain rule:

`4x-14y(dy)/dx=0`

`rArr 14y*(dy)/dx=4x`

`rArr (dy)/dx=(4x)/14y=(2x)/(7y)`

Now for the second deriative apply the quotient rule:

`(d^2y)/dx^2=(7y*2-2x*7(dy)/dx)/(7y)^2`

`=(14y-14xdy/dx)/(49y^2)`

Substituting the value of `(dy)/dx`

`(d^2y)/dx^2=(14y-14x*(2x)/(7y))/(49y^2)`

`=2/(7y)-(4x^2)/(49y^3)`

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