Chapter 3.9 - Hyperbolic Functions

sinhx

sinhx

(e^x-e^-x)/2

coshx

(e^x+e^-x)/2

tanhx

sinhx/coshx

cschx

1/sinhx

sechx

1/coshx

cothx

coshx/sinhx

sinh(-x)

-sinh(x)

cosh²x-sinh²x

1

sinh(x+y)

sinhxcoshy+coshxsinhy

cosh(x+y)

coshxcoshy+sinhxsinhy

cosh(-x)

coshx

1-tanh²x

sech²x

d/dx(sinhx)

coshx

d/dx(coshx)

sinhx

d/dx(tanhx)

sech²x

d/dx(cschx)

-cschxcothx

d/dx(sechx)

-sechxtanhx

d/dx(cothx)

-csch²x

sinh^-1(x)

ln(x+sqrt(x²+1))

cosh^-1(x)

ln(x+sqrt(x²-1))

tanh(-1)x

(1/2)(ln((1+x)/(1-x)))

d/dx(sinh^-1(x))

1/sqrt(1+x²)

d/dx(cosh^-1(x))

1/sqrt(x²-1)

d/dx(tanh^-1(x))

1/(1-x²)

d/dx(csch^-1(x))

-1/(abs(x)sqrt(x²+1))

d/dx(sech^-1(x))

-1/(xsqrt(1-x²))

d/dx(coth^-1(x))

1/(1-x²)