I am deriving a partial differential equation for wave in a string. $f$ represents displacement of the string at point $z$. I am stuck at a step.
Can anyone help me, how $ \left.\dfrac{\partial f}{\partial z} \right\arrowvert_{z+\Delta z} - \left.\dfrac{\partial f}{\partial z} \right\arrowvert_{z} $ can be reduced to $ \dfrac{\partial^2 f}{\partial z^2} \Delta z$ ?