Differentiating & Integrating Hyperbolic Functions (Edexcel A-Level Further Mathematics): Quizzes

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Differentiating & Integrating Hyperbolic Functions
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What is the logarithmic form of sinh⁡−1x\sinh^{-1} x?

ln⁡(x+x2+1)\ln(x + \sqrt{x^2 + 1})

What is the domain of cosh⁡−1x\cosh^{-1} x?

x≥1x \geq 1

What is ddx[arcsin⁡(x)]\frac{d}{dx}[\arcsin(x)]?

11−x2\frac{1}{\sqrt{1 - x^2}}

What is ddx[arccos⁡(x)]\frac{d}{dx}[\arccos(x)]?

−11−x2-\frac{1}{\sqrt{1 - x^2}}

What is the domain of tanh⁡−1x\tanh^{-1} x?

∣x∣<1|x| < 1

What is ddx[arsinh(x)]\frac{d}{dx}[\text{arsinh}(x)]?

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

What is the logarithmic form of tanh⁡−1x\tanh^{-1} x?

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

What is ddx[arctan⁡(x)]\frac{d}{dx}[\arctan(x)]?

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

Which square root is used in cosh⁡−1x\cosh^{-1} x?

x2−1\sqrt{x^2 - 1}

What trigonometric identity is used when differentiating arsinh(tan⁡x)\text{arsinh}(\tan x)?

1+tan⁡2x=sec⁡2x1 + \tan^2 x = \sec^2 x

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