Differentiation Notations ================================ Leibniz's Notation ------------------- The derivative of a function :math:`f` at :math:`x` is given by :math:`\lim\limits_{h\to0} \frac{f(x+h)-f(x)}{h}`. The Leibniz's notation expresses the derivative of :math:`f` as :math:`\frac{dy}{dx}` with :math:`y=f(x)`. More details `here `__. .. note:: The following :math:`\frac{dx}{dt}` means :math:`x` is a function of :math:`t` such as :math:`x=f(t)`. See explanations `here `__. Lagrange's Notation ------------------- Also cal prime notation Newton's Notation ------------------- .. note:: These notes are inspired from `this page `__