Derivatives of Inverse Trig Functions
Derivatives of Inverse Trig Functions
Derivatives of Inverse Trig Functions
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We list the derivatives <strong>of</strong> the six inverse trigonometricfunctions...(arcsin, arccos, arctan, arccsc, arcsec, arccot)In each case u denotes a differentiable function <strong>of</strong> x.There is no common agreement on the definition <strong>of</strong> arcsecx (or arccsc x) for negative values <strong>of</strong> x. When we definedthe range <strong>of</strong> arcsec x, we chose to preserve the identityarcsec x = arccos (1/x). One <strong>of</strong> the consequences <strong>of</strong> thischoice is that the slope <strong>of</strong> the graph <strong>of</strong> the inverse secantfunction is always positive, which accounts for theabsolute value sign in the formulafor the derivative <strong>of</strong> arcsec x.6
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