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I was just having some trouble with the derivatives of Inverse Hyperbolic function,, especially the Tan hyperbolic inverse and the Cotan hyperbolic inverse, they both have the same derivative but their graphs are different. And i was thinking, how can functions having different graphs have the same derivatives?

Sorry for, me being a bit dumb, in-case....

REGARDS!!

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1 Answer

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Hint: We have $\operatorname{artanh}(0)=0$ and $\operatorname{arcoth}(0)$ doesn't exist, so they cannot have the same derivative.

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