differentiating-and-integrating-hyperbolic-functions

Differentiating hyperbolic functions

What are the derivatives of the hyperbolic functions?

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• These are given in the formulae booklet

  • You can prove them by differentiating the definitions involving e

• Notice that they are similar to the derivatives of the circular trig functions

  • Be careful of the difference between the derivatives of cosx and coshx

    • One involves a negative sign and the other does not

How do I differentiate expressions involving hyperbolic functions?

• The following differentiation skills may be required

  • Chain rule

  • Product rule

  • Quotient rule

  • Implicit differentiation

• Questions may involve showing or proving given results or finding unknown constants

• It is common that derivatives can be written in terms of the original function

  • This is due to the derivative of e^x also being e^x giving rise to the repetition of terms

What are the derivatives of the inverse hyperbolic functions?

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