```math v=\sqrt{\frac{F}{\mu}}=\sqrt{\frac{\frac{mgh}{L}}{\frac{m}{L}}}=\sqrt{gh}\\ a=\frac{dv}{dt}=\frac{dv}{dh}\cdot\frac{dh}{dt}=\frac{1}{2}\sqrt{\frac{g}{h}}\cdot\sqrt{gh}=\frac{1}{2}g=\frac{g}{2}\\ d\frac{e^x}{dx}=\lim_{\Delta x\rightarrow0}\frac{e^{x+\Delta x}-e^x}{(x+\Delta x)-x}=\lim_{\Delta x\rightarrow0}\frac{e^x(e^{\Delta x}-1)}{\Delta x}=e^x\lim_{\Delta x\rightarrow0}\frac{(1+\Delta x)^{\frac{1}{\Delta x}\Delta x}-1}{\Delta x}=e^x\lim_{\Delta x\rightarrow0}\frac{1+\Delta x-1}{\Delta x}=e^x \\\aleph ```