HyperbolicFunctions - Hyperbolic Functions Hyperbolic...

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Hyperbolic Functions Hyperbolic cosine of x : cosh 2 x x e e x - + = Hyperbolic sine of x : sinh 2 x x e e x - - = Hyperbolic tangent: sinh tanh cosh x x x x x e e x x e e - - - = = + Hyperbolic cotangent: cosh coth sinh x x x x x e e x x e e - - + = = - Hyperbolic secant: 1 2 sech cosh x x x x e e - = = + Hyperbolic cosecant: 1 2 csch sinh x x x x e e - = = - Identities 2 2 2 2 2 2 sinh cosh cosh sinh 1 tanh sech 1 coth csch 1 x x x e x x x x x x + = - = = - = + Derivatives ( 29 ( 29 ( 29 2 sinh cosh cosh sinh tanh sech d du u u dx dx d du u u dx dx d du u u dx dx = = = ( 29 ( 29 ( 29 2 coth csch sech sech tanh csch csch coth d du u u dx dx d du u u u dx dx d du u u u dx dx = - = - = - Integrals 2 sinh cosh cosh sinh sech tanh u du u C u du u C u du u C = + = + = + 2 csch coth sech tanh sech csch coth csch u du u C u u du u C u u du u C = - + = - + = - + Useful Identities 1 1 1 sech cosh x x - - = 1 1 1 csch sinh x x - - = 1 1 1 coth tanh x x - - = Derivatives of Inverse Logarithm Formulas for Evaluating Hyperbolic Functions Inverse Hyperbolic Functions ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 2 1 2 1 2 1 2 1 2 sinh 1 1 cosh 1 , 1 1 tanh 1 , 1 1 coth 1 , 1 1 sech 1 , 0 1 1 csch 1 , 0 1 d u du dx dx u d u du u dx dx u d u du u dx u dx d u du u dx u dx d u du u dx dx u u d u du u dx dx u u - - - - - - = + = - = < - = - - = < < - - = + ( 29 ( 29 1 2 1 2 1 2 1 2 1 1 sinh ln , 1 cosh ln , 1 1 1 1 tanh ln , 1 2 1 1 1 sech
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