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Hyperbolic Functions

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Derivative of Hyperbolic Sine

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The derivative of sinh(x)\sinh(x) is cosh(x)\cosh(x).

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Derivative of Hyperbolic Cosine

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The derivative of cosh(x)\cosh(x) is sinh(x)\sinh(x).

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Integral of Hyperbolic Sine

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The integral of sinh(x)\sinh(x) is cosh(x)+C\cosh(x) + C.

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Integral of Hyperbolic Cosine

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The integral of cosh(x)\cosh(x) is sinh(x)+C\sinh(x) + C.

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Derivative of Hyperbolic Tangent

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The derivative of tanh(x)\tanh(x) is sech2(x)\text{sech}^2(x).

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Integral of Hyperbolic Tangent

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The integral of tanh(x)\tanh(x) is lncosh(x)+C\ln |\cosh(x)| + C.

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Derivative of Hyperbolic Secant

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The derivative of sech(x)\text{sech}(x) is sech(x)tanh(x)-\text{sech}(x)\tanh(x).

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Integral of Hyperbolic Secant

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The integral of sech(x)\text{sech}(x) is 2arctan(ex)+C2\arctan(e^x) + C.

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Derivative of Hyperbolic Cosecant

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The derivative of csch(x)\text{csch}(x) is csch(x)coth(x)-\text{csch}(x)\coth(x).

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Integral of Hyperbolic Cosecant

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The integral of csch(x)\text{csch}(x) is lntanh(x/2)+C\ln |\tanh(x/2)| + C.

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