Hyperbolic Functions

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Last updated 11:15 PM on 9/3/26
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17 Terms

1
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d/dx(arcsinhx)

1 / (1+x²)^1/2

2
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d/dx(arccoshx)

1 / (x²-1)^1/2

3
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d/dx(arctanhx)

1 / (1-x²)

4
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(a²-x²)^1/2

x=atanh(theta)

5
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(x²-a²)^1/2

x=acosh(theta)

6
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(x²+a²)^1/2 or (a²+x²)^1/2

x=asinh(theta)

7
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sinhx

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

8
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coshx

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

9
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cosh²x - sinh²x = 1

yep

10
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d/dx(coshx)

sinhx

11
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d/dx(sinhx)

coshx

12
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d/dx(tanhx)

sech²x

13
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d/dx(cothx)

-csch²x

14
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d/dx(sechx)

-sechxtanhx

15
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d/dx(cschx)

-cschxcothx

16
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sinh²x

(cosh2x - 1) / 2

17
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cosh²x

(cosh2x + 1) / 2