FP2 differentiating hyperbolic functions Watch

crazylady_012
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#1
Report Thread starter 8 years ago
#1
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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spread_logic_not_hate
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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.
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nuodai
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Report 8 years ago
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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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