People living at Mars, instead of the usual definition of derivative D f(x), define a new…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
People living at Mars, instead of the usual definition of derivative D f(x), define a new kind of derivative, D*f(x) by the formula
\(D^{*} f(x)=\lim _{h \rightarrow 0} \frac{f^{2}(x+h)-f^{2}(x)}{h}\)where f2 (x) means [f (x)]2. If f (x) = x lnx then
\(\left.D * f(x)\right|_{x=e}\) has the value
\(D^{*} f(x)=\lim _{h \rightarrow 0} \frac{f^{2}(x+h)-f^{2}(x)}{h}\)where f2 (x) means [f (x)]2. If f (x) = x lnx then
\(\left.D * f(x)\right|_{x=e}\) has the value
- e
- 2e
- 4e
- 8 e
Answer
(C) 4e
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