Chapter 6 | Applications of Integration
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Figure 6.82 Graphs of the inverse hyperbolic functions.
To find the derivatives of the inverse functions, we use implicit differentiation. We have y = sinh −1 x sinh y = x d dx sinh y = d dx x cosh y dy dx = 1. Recall that cosh 2 y −sinh 2 y =1, so cosh y = 1+sinh 2 y . Then, dy dx = 1 cosh y = 1 1+sinh 2 y = 1 1+ x 2 . We can derive differentiation formulas for the other inverse hyperbolic functions in a similar fashion. These differentiation formulas are summarized in the following table.
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