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    Hi, just started FP2 and have a question but havent got a clue how to do it.
    Show that d sin^-1(tanhx) =sechx
    dx
    Could anyone give me a hand how to start it please?
    Thank you for any help in advance.
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    Differentiating hyperbolic functions is identical to differentiating normal trig functions, except that you need to bear Osborne's rule in mind.

    http://mathworld.wolfram.com/OsbornesRule.html

    With your example, slightly more complex - try writing the expression as

     sin y = tanh x

    and implicitly differentiate.
    • PS Helper
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    You can break down the problem by letting y = \sin^{-1}(\tanh x). Now, if you know how to differentiate \sin^{-1} x, then you can use the chain rule. If you don't know how to do that, work out how and then use the chain rule :p:
 
 
 
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