What are the derivatives of the six basic hyperbolic functions?

Nannie Mack

Nannie Mack

Answered question

2021-10-12

What are the derivatives of the six basic hyperbolic functions? What are the corresponding integral formulas? What similarities do you see here to the six basic trigonometric functions?

Answer & Explanation

Brighton

Brighton

Skilled2021-10-13Added 103 answers

Step 1
Derivatives of the six basic hyperbolic functions:
d(sinhx)dx=coshx
d(coshx)dx=sinhx
d(tanhx)dx=sech2x
d(sechx)dx=sechxtanhx
d(cschx)dx=cschxcoshx
d(coshx)dx=csch2x
Step 2
Integrals of the six basic hyperbolic functions:
sinhxdx=coshx+C
coshxdx=sinhx+C
tanhxdx=lnmidcoshxmid+C
cschxdx=lntanh(x/2)+C
sechxdx=tan1(sinhx)+C
cothxdx=lnsinhx+C
Similarities are the derivative and integral of sinh x&cosh x are same.

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