Determine whether the statement is true or false. d^2y/dx^2 = (dy/dx)^2

Answer 1

The operations are very different: (dy/dx)²=(dy/dx)(dy/dx), whereas d²y/dx² iis operation to differentiate two times, that is, consecutive to make the second derivative

Answer 2

This is not true becouse left side is the second derivative y'', but right side is squere of 1st derivative (y')²,

and this is not alvays true.

For example if y = x, then y'' = 0 but (y')² = 1