"f'(x)" is read "f prime of x" or "the derivative of f of x" or "the derivative of f with respect to x".

"f''(x)" is read "f double prime of x" or "the second derivative of f of x" or "the second derivative of f with respect to x".

"ẋ" is read "x dot" or "the derivative of x with respect to time" or "the time derivative of x".

"ẍ" is read "x double dot" or "the second derivative of x with respect to time".