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  5. Applications of Derivatives

12th Class Mathematics Applications of Derivatives Question Bank Case Based (MCQs) - Derivatives

  • question_answer
    The derivative of \[{{\cos }^{-1}}\left( 2x-1 \right)\]w.r.t. \[{{\cos }^{-1}}x\]is

    A) 2

    B) \[\frac{-1}{2\sqrt{1-{{x}^{2}}}}\]

    C) \[\frac{2}{x}\]

    D) \[1-{{x}^{2}}\]

    Correct Answer: A

    Solution :

    Let \[y={{\cos }^{-1}}\left( 2{{x}^{2}}-1 \right)=2{{\cos }^{-1}}x\] Differentiating w.r.t \[{{\cos }^{-1}}\,x\], we get \[\frac{dy}{d\left( {{\cos }^{-1}}x \right)}=\frac{2d\left( {{\cos }^{-1}}x \right)}{d\left( {{\cos }^{-1}} \right)}=2\]


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