The second derivative of the following: y = e^(-2x^2)

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By taking the first derivative, we have

`dy/dx = d/dx[e^-2^(x^2)]`

     `=[e^-2^(x^2)]*d/dx(-2x^2)`

     `=[e^-2^(x^2)]*(-2*2x^(2-1))`

    `=[e^-2^(x^2)]*(-4x) or-4x[e^-2^(x^2)]`

So the second derivative will be

`(d^2y)/dx^2 = -4[x*d/dx[e^-2^(x^2)]+[e^-2^(x^2)]*d/dx(x)]`

`(d^2y)/dx^2 = -4[x*[e^-2^(x^2)]*d/dx(-2x^2)+[e^-2^(x^2)]*1]` 

`(d^2y)/dx^2 = -4[x*[e^-2^(x^2)]*(-4x)+[e^-2^(x^2)]]` 

`(d^2y)/dx^2 = -4[e^-2^(x^2)](-4x^2+1)`

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