Hyperbolic Functions (AQA A-Level Further Maths): Flashcards

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Hyperbolic Functions
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ddx(sinh⁡x)\frac{d}{dx}(\sinh x)

cosh⁡x\cosh x

ddx(cosh⁡x)\frac{d}{dx}(\cosh x)

sinh⁡x\sinh x

ddx(tanh⁡x)\frac{d}{dx}(\tanh x)

sech⁡2x\operatorname{sech}^2 x

∫sinh⁡x dx\int \sinh x \, dx

cosh⁡x+c\cosh x + c

∫tanh⁡x dx\int \tanh x \, dx

ln⁡cosh⁡x+c\ln \cosh x + c

ddx(sech⁡x)\frac{d}{dx}(\operatorname{sech} x)

−sech⁡xtanh⁡x-\operatorname{sech} x \tanh x

ddx(coth⁡x)\frac{d}{dx}(\operatorname{coth} x)

−cosech⁡2x-\operatorname{cosech}^2 x

ddx(arcosh x)\frac{d}{dx}(\text{arcosh } x)

1x2−1\frac{1}{\sqrt{x^2 - 1}}

ddx(arsinh x)\frac{d}{dx}(\text{arsinh } x)

1x2+1\frac{1}{\sqrt{x^2 + 1}}

Substitution for x2+a2\sqrt{x^2 + a^2}

x=asinh⁡ux = a\sinh u

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