Table 2.8.1 contains a graph of the principal branch for each of the six trig functions, and the graph of the corresponding inverse function.
Principal Branch
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Principal Domain
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Inverse Function
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Table 2.8.1 Principal branches of the trig functions, and their inverse functions
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Table 2.8.2 lists the derivatives of the six inverse trigonometric functions.
Function
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Maple's Derivative
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Textbook Derivative
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arcsine
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=
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,
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arccosine
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=
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,
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arctangent
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=
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arccotangent
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=
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arcsecant
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=
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,
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arccosecant
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=
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,
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Table 2.8.2 Derivatives of the six inverse trigonometric functions
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Maple's differentiation formulas are correct for complex, but in the typical calculus text, the formulas are stated for real. That is why the textbook formulas have restrictions and vary slightly from the Maple form.
The second column in the table uses the formal name of each inverse function. However, in 2D math mode, Maple understands the usage for , etc.