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Edexcel IAL Mathematics A2 FP3.1.2 inverse hyperbolic functions

Edexcel IAL Mathematics A2 FP3.1.2 inverse hyperbolic functions
Pearson Edexcel IAL Mathematics syllabusMathematics YMA01First assessment 2019

Only two direct questions exist, so keep the transfer narrow: derive the correct logarithmic branch, then use sinh identities to give exact intersection coordinates.

How this is tested

  • Derive inverse hyperbolic log forms by solving the exponential quadratic branch.
  • Use sinh 3x identities to find intersections and express coordinates as logs.

Question 4(i)

f(x)=xarccos⁡x−1⩽x⩽1f(x)=x \arccos x \quad-1 \leqslant x \leqslant 1

Find the exact value of f′(0.5)\mathrm{f}^{\prime}(0.5).