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mathcalculuscalculus questions and answers1. the hyperbolic functions cosh and sinh are defined by the formulas e² e cosh(z) e² te 2 sinh(r) 2 the functions tanh, coth, sech and esch are defined in terms of cosh and sinh analogously to how they are for trigonometric functions: tanh(r)= sinh(r) cosh(z)' coth(z) = cosh(z) sinh(r) sech(z) 1 cosh(z)' csch(z) = sinh(r) (a) find formulas for the
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Question: 1. The Hyperbolic Functions Cosh And Sinh Are Defined By The Formulas E² E Cosh(Z) E² Te 2 Sinh(R) 2 The Functions Tanh, Coth, Sech And Esch Are Defined In Terms Of Cosh And Sinh Analogously To How They Are For Trigonometric Functions: Tanh(R)= Sinh(R) Cosh(Z)' Coth(Z) = Cosh(Z) Sinh(R) Sech(Z) 1 Cosh(Z)' Csch(Z) = Sinh(R) (A) Find Formulas For The
1. The hyperbolic functions cosh and sinh are defined by the formulas
e² e
cosh(z)
e² te
2
sinh(r)
2
The functions tanh, coth
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Transcribed image text: 1. The hyperbolic functions cosh and sinh are defined by the formulas e² e cosh(z) e² te 2 sinh(r) 2 The functions tanh, coth, sech and esch are defined in terms of cosh and sinh analogously to how they are for trigonometric functions: tanh(r)= sinh(r) cosh(z)' coth(z) = cosh(z) sinh(r) sech(z) 1 cosh(z)' csch(z) = sinh(r) (a) Find formulas for the derivatives of all six of these functions. You must show all of your work. (b) The function sinh is one-to-one on R, and its range is R, so it has an inverse defined on R, which we call arcsinh. Use implicit differentiation to prove that 1 (arcsinh(r)) = x² + =