JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
     \[\frac{d}{dx}\cos \,{{\text{h}}^{-1}}(\sec x)=\]                                                           [RPET 1997]

    A)            sec x

    B)            sin x

    C)            tan x

    D)            cosec x

    Correct Answer: A

    Solution :

               \[\frac{d}{dx}{{\cosh }^{-1}}(\sec x)\]\[=\frac{1}{\sqrt{{{\sec }^{2}}x-1}}\frac{d}{dx}\sec x\]                                                                             \[=\frac{1}{\tan x}.\sec x.\tan x=\sec x\].


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