Derivatives of Inverse Trigonometric Functions

Proposition (Derivatives of the Inverse Trigonometric Functions) The inverse trigonometric functions arcsine, arccosine, arctangent, arccotangent, arccosecant, and arcsecant are all differentiable functions on their domain and their derivative functions are:

        

        

    

Example (Derivatives of the Inverse Trigonometric Functions) Find the derivative of the function

    Solution. Using the product rule and the derivative formulas for arcsine and arccosine we determine:





Example (Derivatives of the Inverse Trigonometric Functions) Find the derivative of the function

    Solution. Using the product rule and the derivative formulas for arctangent and arccotangent we determine:
    
         



Example (Derivatives of the Inverse Trigonometric Functions) Find the derivative of the function

    Solution. Using the product rule and the derivative formulas for arctangent and arcsecant we determine:
    



Example (Derivatives of the Inverse Trigonometric Functions) Find the derivative of the function ;      

    Solution. Using the quotient rule, the derivative formulas for arcsine and arccosine and some trigonometric identities, we determine:     







Recall, the cofunction theorem from trigonometry: if and then if and only if

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Derivatives Of Inverse Trigonometric Functions
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
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