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.

Q1:

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

Q2:

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

Q3:

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

Q4:

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

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

Q5:

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‘₯

Q6:

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

Q7:

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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