Hyperbolic Functions (Edexcel A-Level Further Mathematics): Flashcards

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Differentiating & Integrating Hyperbolic Functions
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Logarithmic form of sinh⁡−1x\sinh^{-1} x

ln⁡(x+x2+1)\ln(x + \sqrt{x^2 + 1})

Logarithmic form of cosh⁡−1x\cosh^{-1} x

ln⁡(x+x2−1)\ln(x + \sqrt{x^2 - 1})

Logarithmic form of tanh⁡−1x\tanh^{-1} x

12ln⁡(1+x1−x)\frac{1}{2} \ln\left(\frac{1 + x}{1 - x}\right)

Derivative of arcsin⁡(x)\arcsin(x)

11−x2\frac{1}{\sqrt{1 - x^2}}

Derivative of arccos⁡(x)\arccos(x)

−11−x2\frac{-1}{\sqrt{1 - x^2}}

Derivative of arsinh(x)\text{arsinh}(x)

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

Derivative of arctan⁡(x)\arctan(x)

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

Domain of cosh⁡−1x\cosh^{-1} x

x≥1x \geq 1

Domain of tanh⁡−1x\tanh^{-1} x

∣x∣<1|x| < 1

Hyperbolic identity: cosh⁡2(y)−sinh⁡2(y)=?\cosh^2(y) - \sinh^2(y) = ?

11

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