Worksheet: Derivatives of Inverse Hyperbolic Functions

In this worksheet, we will practice finding the derivatives of inverse hyperbolic functions and using rules of differentiation with them.


Find the derivative of the function 𝑦=√π‘₯cosh.

  • A1√π‘₯√π‘₯+1
  • Bβˆ’12√π‘₯√π‘₯+1
  • C12√π‘₯√π‘₯βˆ’1
  • D1√π‘₯βˆ’1
  • E12√π‘₯√π‘₯+1


Find the derivative of the function 𝑦=π‘₯ο€»π‘₯3ο‡βˆ’βˆš9+π‘₯sinh.

  • AsinhοŠ±οŠ§ο€»π‘₯3
  • BsinhοŠ±οŠ§οŠ¨ο€»π‘₯3+2π‘₯9+π‘₯
  • CsinhοŠ±οŠ§οŠ¨ο€»π‘₯3ο‡βˆ’2π‘₯9+π‘₯
  • DsinhοŠ±οŠ§οŠ¨οŠ¨ο€»π‘₯3ο‡βˆ’π‘₯9βˆ’π‘₯+π‘₯9+π‘₯
  • EsinhοŠ±οŠ§οŠ¨οŠ¨ο€»π‘₯3+π‘₯3√π‘₯+1+π‘₯√π‘₯+9


Find the derivative of the function 𝑦=(π‘₯)sinhtan.

  • Asectanπ‘₯√π‘₯βˆ’1
  • Bβˆ’π‘₯√1βˆ’π‘₯sectan
  • Csectanπ‘₯1βˆ’π‘₯
  • D|π‘₯|sec
  • Eβˆ’π‘₯sec


Find the derivative of the function 𝑦=(π‘₯)cothsec.

  • Aβˆ’π‘₯sec
  • Bcotπ‘₯
  • Cβˆ’π‘₯csc
  • Dcscπ‘₯
  • Esecπ‘₯


Find the derivative of tanh(π‘₯) by using the inverse function theorem together with the facts that ddtanhcoshπ‘₯π‘₯=1π‘₯ and coshsinhπ‘₯βˆ’π‘₯=1.

  • A11βˆ’π‘₯
  • B11+π‘₯
  • Ccoshπ‘₯
  • D1π‘₯βˆ’1
  • Esinhπ‘₯


Find the derivative of the function 𝑦=π‘₯π‘₯+√1βˆ’π‘₯tanhln.

  • Atanhπ‘₯+2π‘₯1βˆ’π‘₯
  • Btanhπ‘₯
  • Ctanhπ‘₯+2π‘₯√1βˆ’π‘₯+π‘₯1βˆ’π‘₯
  • Dtanhπ‘₯βˆ’2π‘₯1βˆ’π‘₯
  • Eβˆ’π‘₯tanh


Find the derivative of the function 𝑦=𝑒sechοŠ±οŠ§οŠ±ο—.

  • A1√1+π‘’οŠ±οŠ¨ο—
  • B𝑒π‘₯√1βˆ’π‘₯οŠ±ο—οŠ¨
  • Cπ‘’βˆš1βˆ’π‘’οŠ±ο—οŠ±οŠ¨ο—
  • Dβˆ’1√1βˆ’π‘’οŠ±οŠ¨ο—
  • E1√1βˆ’π‘’οŠ±οŠ¨ο—

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