MATH 241 Section 3.11 Page 1
Definition of Hyperbolic Functions
2
ee
sinh xx
x
−
−
= x
x sinh
1
csch =
2
ee
cosh xx
x
−
+
= x
x cosh
1
sec =
x
x
x cosh
sinh
tanh = x
x
x sinh
cosh
coth =
Hyperbolic Identities
x - -x )(sinh)(sinh = x- x 1 sinh cosh 22 =
x -x )(cosh)(cosh =x x 22 sechtanh - 1 =
)(sinh)(cosh)(cosh)(sinh)(sinh y x y x yx
+
=+
)(sinh)(sinh)(cosh)(cosh)(cosh y x y x yx
+
=+
Derivatives of Hyperbolic Functions
x x cosh)(sinh
dx
d= x x - x cothcsch)(csch
dx
d=
x x sinh)(cosh
dx
d= x x - x tanhsech)(sech
dx
d=
x x 2
sech)(tanh
dx
d= x - x 2
csch)(coth
dx
d=
