Hyperbolic functions
Identities
sinh (x + y) = sinh (x) cosh (y) + cosh (x) sinh (y)
cosh (x + y) = cosh (x) cosh (y) + sinh (x) sinh (y)
Reciprocal
coth^2 (x) - 1 = cosech^2 (x)
1 - tanh^2 (x) = sech^2 (x)
Calculus
Differentiation
d/dx cosh x = sinh x
d/dx cosech x = -cosech (x) coth (x)
d/dx sech x = -sech (x) tanh (x)
d/dx coth x = -cosech^2 x
Graphs
sinh x
cosh x
tanh x
arcsinh x
arcosh x
arctanh x
Double angle
tanh (2x) = 2tanh (x)/1+tanh^2 (x)
d/dx sinh x = cosh x
Integration
∫ tanh x dx = ln|cosh x| + c
d/dx tanh x = sech^2 x
∫ coth x dx = ln|sinh x| + c