Register  
 
 About Us | Help | Sign in
 
HomeForumsArticlesRevision NotesPersonal StatementsUniversity GuidesHealth & RelationshipsCareers
Create New Article | Editing Help  
   

Advanced Search
Revision:Differentiation of Hyperbolic Functions

From The Student Room

(Redirected from Differentiation)

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Differentiation of Hyperbolic Functions

Derivatives of Hyperbolic Functions

\dfrac{\text{d}}{\text{d} x}(\sinh x) = \cosh x


\dfrac{\text{d}}{\text{d} x}(\cosh x) = \sinh x


\dfrac{\text{d}}{\text{d} x}(\tanh x) = \mathrm{sech} ^2x


\dfrac{\text{d}}{\text{d} x}(\mathrm{sech} x) = -\mathrm{sech} x\tanh x


\dfrac{\text{d}}{\text{d} x}(\mathrm{cosech} x) = -\mathrm{cosech} x\coth x


\dfrac{\text{d}}{\text{d} x}(\coth x) = -\mathrm{cosech} ^2x


Derivatives of Inverse Hyperbolic Functions

\dfrac{\text{d}}{\text{d} x}(\mathrm{arsinh} x) = \dfrac{1}{\sqrt{x^2+1}}


\dfrac{\text{d}}{\text{d} x}(\mathrm{arcosh} x) = \dfrac{1}{\sqrt{x^2-1}}


\dfrac{\text{d}}{\text{d} x}(\mathrm{artanh} x) = \dfrac{1}{1-x^2}

Derivatives of Inverse Trigonometric Functions

\dfrac{\text{d}}{\text{d} x}(\arcsin x) = \dfrac{1}{\sqrt{1-x^2}}


\dfrac{\text{d}}{\text{d} x}(\arccos x) = \dfrac{-1}{\sqrt{1-x^2}}


\dfrac{\text{d}}{\text{d} x}(\arctan x) = \dfrac{1}{1+x^2}

Retrieved from "http://thestudentroom.co.uk/wiki/Revision:Differentiation_of_Hyperbolic_Functions"
Article Tools:  Create New Article  |  Report This Article  |  This Article's History  | 
collapse
Recent Threads
 
collapse Would you rather live in the US or the UK?
started by: SusanDoran
replies: 15
last post: 1 Minute Ago
collapse Do you know your IQ?
started by: k9ruby
replies: 77
last post: 1 Minute Ago
collapse Compulsory A-levels
started by: Jimlon0
replies: 9
last post: 1 Minute Ago
collapse Credit Expert
started by: SmilerNuts
replies: 3
last post: 1 Minute Ago
collapse Wireless Problems
started by: Lucy :)
forum: Technology
replies: 35
last post: 1 Minute Ago