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People living at Mars, instead of the usual definition of derivative `Df(x)`, define a new kind of derivative `D`*`f(x)` by the formula `D`*`f(x)` = `Lim_(h->0) (f^2(x+h) - f^2(x))/h` where `f^2(x)` means `[f(x)]^2`. If `f(x)=x ln x` then `D`*`f(x)|_(x=e)` has the value `(A)``e` `(B)` `2e` `(C)` `4e` `(D)` none

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Step by step text solution for People living at Mars, instead of the usual definition of derivative Df(x), define a new kind of derivative D*f(x) by the formula D*f(x) = Lim_(h->0) (f^2(x+h) - f^2(x))/h where f^2(x) means [f(x)]^2. If f(x)=x ln x then D*f(x)|_(x=e) has the value (A)e (B) 2e (C) 4e (D) none by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Knowledge Check

  • Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D**F(x) by the formula D** (x) = lim_( h to 0) ( f^(2) ( x + h) - f^(2) (x))/( h) , where f^(2) (x) means [ f (x)]^(2) and if f(x) = x log x, then D** f(x) |_(x = e) has the value

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