Hàm số đường cong ex thuận Đạo hàm hàm số ${\displaystyle \sinh x}$ ${\displaystyle \cosh x={\frac {e^{x}+e^{-x}}{2}}}$ ${\displaystyle \cosh x}$ ${\displaystyle \sinh x={\frac {e^{x}-e^{-x}}{2}}}$ ${\displaystyle \tanh x}$ ${\displaystyle {\operatorname {sech} ^{2}\,x}}$ ${\displaystyle \operatorname {sech} \,x}$ ${\displaystyle -\tanh x\,\operatorname {sech} \,x}$ ${\displaystyle \operatorname {csch} \,x}$ ${\displaystyle -\,\operatorname {coth} \,x\,\operatorname {csch} \,x}$ ${\displaystyle \operatorname {coth} \,x}$ ${\displaystyle -\,\operatorname {csch} ^{2}\,x}$
 Hàm số đường cong ex nghịch Đạo hàm của hàm số ${\displaystyle \operatorname {arsinh} \,x}$ ${\displaystyle {1 \over {\sqrt {x^{2}+1}}}}$ ${\displaystyle \operatorname {arcosh} \,x}$ ${\displaystyle {\frac {1}{\sqrt {x^{2}-1}}}}$ ${\displaystyle \operatorname {artanh} \,x}$ ${\displaystyle {1 \over 1-x^{2}}}$ ${\displaystyle \operatorname {arsech} \,x}$ ${\displaystyle -{1 \over x{\sqrt {1-x^{2}}}}}$ ${\displaystyle \operatorname {arcsch} \,x}$ ${\displaystyle -{1 \over |x|{\sqrt {1+x^{2}}}}}$ ${\displaystyle \operatorname {arcoth} \,x}$ ${\displaystyle {1 \over 1-x^{2}}}$