CAIE A-Level Further Math A2 2.3.1 Hyperbolic Functions QuestionsPractise differentiating hyperbolic and inverse hyperbolic functions, including parametric forms, with Further Mathematics Paper 2 questions and mark schemes.Syllabus2028–2030CourseFurther Mathematics 9231LevelA2
CAIE A-Level Further Math A2 2.3.1 Hyperbolic Functions Questions question 1[Maximum number: 3]Show that dy dx=−cosechx\frac{\mathrm{d} y}{\mathrm{~d} x}=-\operatorname{cosech} x dxdy=−cosechx.Show Answerdy dx=−sech2(12x)2tanh(12x)=−12sinh(12x)cosh(12x) Or dy dx=−cosech2(12x)2coth(12x)=−12sinh(12x)cosh(12x)\begin{aligned} \frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{\operatorname{sech}^{2}\left(\frac{1}{2} x\right)}{2 \tanh \left(\frac{1}{2} x\right)}=-\frac{1}{2 \sinh \left(\frac{1}{2} x\right) \cosh \left(\frac{1}{2} x\right)} \text { Or } \frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{\operatorname{cosech}^{2}\left(\frac{1}{2} x\right)}{2 \operatorname{coth}\left(\frac{1}{2} x\right)}=-\frac{1}{2 \sinh \left(\frac{1}{2} x\right) \cosh \left(\frac{1}{2} x\right)} \end{aligned} dxdy=−2tanh(21x)sech2(21x)=−2sinh(21x)cosh(21x)1 Or dxdy=−2coth(21x)cosech2(21x)=−2sinh(21x)cosh(21x)1Uses chain rule.=−1sinh(x)=−cosechx=-\frac{1}{\sinh (x)}=-\operatorname{cosech} x=−sinh(x)1=−cosechxAG3Add to Test