ALGEBRA      DERIVATIVES      INTEGRALS      SERIES/SEQUENCES      TRIG       
   

   DERIVATIVES > Hyperbolic functions        

Derivatives of hyperbolic functions

{d \over dx} \sinh x = \cosh x

{d \over dx} \cosh x = \sinh x

{d \over dx} \tanh x = \mbox{sech}^2\,x

{d \over dx} \,\mbox{sech}\,x = -\tanh x\,\mbox{sech}\,x

{d \over dx} \,\mbox{coth}\,x = -\,\mbox{csch}^2\,x

{d \over dx} \,\mbox{csch}\,x = -\,\mbox{coth}\,x\,\mbox{csch}\,x

{d \over dx} \sinh^{-1} x = { 1 \over \sqrt{x^2 + 1}}

{d \over dx} \cosh^{-1} x = {-1 \over \sqrt{x^2 - 1}}

{d \over dx} \tanh^{-1} x = { 1 \over 1 - x^2}

{d \over dx} \mbox{sech}^{-1}\,x = { 1 \over x\sqrt{1 - x^2}}

{d \over dx} \mbox{coth}^{-1}\,x = {-1 \over 1 - x^2}

{d \over dx} \mbox{csch}^{-1}\,x = {-1 \over |x|\sqrt{1 + x^2}}

- DERIVATIVES -
  • Introduction


  • General functions


  • Simple functions


  • Exponential and logarithmic functions


  • Trigonometric functions


  • Hyperbolic functions


    • More