Lesson Worksheet: Derivatives of Hyperbolic Functions Mathematics

In this worksheet, we will practice differentiating hyperbolic functions and using the rules of differentiation like chain rule and product rule with them.

Q1:

Determine and simplify ddsinh𝑥𝑥, where sinh𝑥=𝑒𝑒2 and cosh𝑥=𝑒+𝑒2.

  • Asinh𝑥
  • Bcosh𝑥
  • C𝑥sinh
  • D𝑥cosh
  • Etanh𝑥

Q2:

Determine and simplify ddcoshx𝑥, where sinh𝑥=𝑒𝑒2 and cosh𝑥=𝑒+𝑒2.

  • A𝑥cosh
  • Bsinh𝑥
  • Ccosh𝑥
  • D𝑥sinh
  • Etanh𝑥

Q3:

Find the derivative of tanh𝑥, giving your answer in terms of hyperbolic functions.

  • Asech𝑥
  • B𝑥sech
  • C𝑥sech
  • Dsech𝑥
  • Ecoth𝑥

Q4:

Find the derivative of the function 𝑔(𝑡)=𝑡𝑡+1coth.

  • Acothcsch𝑡+12𝑡𝑡+1𝑡+1
  • Bcothcsch𝑡+1𝑡𝑡+1𝑡+1
  • Ccothsech𝑡+12𝑡𝑡+1𝑡+1
  • Dcothsech𝑡+1+𝑡𝑡+1𝑡+1
  • Ecothcschcoth𝑡+1𝑡𝑡+1𝑡+1𝑡+1

Q5:

Find the derivative of the function (𝑥)=𝑥sinh.

  • A2𝑥𝑥cosh
  • Bcosh𝑥
  • C2𝑥𝑥cosh
  • D𝑥𝑥cosh
  • E2𝑥𝑥cosh

Q6:

Find the derivative of the function 𝑓(𝑡)=1+𝑡1𝑡sinhsinh.

  • A2𝑡𝑡(1𝑡)sinhcoshsinh
  • B2𝑡(1𝑡)coshsinh
  • C2𝑡𝑡1𝑡sinhcoshsinh
  • D2𝑡𝑡(1𝑡)sinhcoshsinh
  • E2𝑡1𝑡coshsinh

Q7:

Find the derivative of the function 𝑔(𝑥)=𝑥sinh.

  • Asinh2𝑥
  • B𝑥2sinh
  • Csinh𝑥
  • D2𝑥𝑥cosh
  • Esinh2𝑥2

Q8:

Find the derivative of the function 𝑓(𝑥)=𝑥tanh.

  • Asech𝑥2𝑥
  • B𝑥2𝑥sech
  • C𝑥2𝑥sech
  • Dsech𝑥𝑥
  • Esech𝑥𝑥

Q9:

Find the derivative of the function 𝑦=𝑥(1+𝑥)sechlnsech.

  • Asechtanhlnsech𝑥𝑥(1𝑥)
  • B𝑥𝑥(2+𝑥)sechtanhlnsech
  • C𝑥𝑥(1𝑥)sechtanhlnsech
  • Dsechtanhlnsech𝑥𝑥(2+𝑥)
  • E𝑥𝑥(1+𝑥)sechtanhlnsech

Q10:

Find the derivative of the function 𝑦=𝑒cosh.

  • A𝑒3𝑥coshsinh
  • B3𝑒3𝑥coshcosh
  • C3𝑒3𝑥coshsinh
  • D3𝑒3𝑥coshcosh
  • E𝑒sinh

This lesson includes 3 additional questions for subscribers.

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