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JEE Main & Advanced Mathematics Differentiation Question Bank Differentiation of implicit function Parametric

  • question_answer
    Let f and g be differentiable functions satisfying \[{g}'(a)=2,\] \[g(a)=b\] and \[fog=I\](identity function). Then \[f'(b)\] is equal to

    A)            \[\frac{1}{2}\]

    B)            2

    C)            \[\frac{2}{3}\]

    D)            None of these

    Correct Answer: A

    Solution :

               \[fog=I\Rightarrow fog(x)=x\]for all x                    Þ  \[f'(g(x))g'x=1\]for all\[x\]                    Þ  \[f'(g(a))=\frac{1}{g'(a)}=\frac{1}{2}\Rightarrow f'(b)=\frac{1}{2}\ \ \ \ \ \ (\because g(a)=b)\].


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