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If f(x)=(log)(x^2)(logx), then f^(prime)...

If `f(x)=(log)_(x^2)(logx),` then `f^(prime)(x)` at `x=e` is 0 (b) 1 (c) `1/e` (d) `1/2e`

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To find the derivative \( f'(x) \) of the function \( f(x) = \log_{x^2}(\log x) \) and evaluate it at \( x = e \), we will follow these steps: ### Step 1: Rewrite the function using logarithm properties The function can be rewritten using the change of base formula for logarithms: \[ f(x) = \frac{\log(\log x)}{\log(x^2)} \] Using the property \( \log(x^2) = 2\log x \), we can simplify this to: ...
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Knowledge Check

  • If f(x)=log_(x^(2))(logx) ,then f '(x)at x= e is

    A
    0
    B
    1
    C
    `(1)/(e )`
    D
    `(1)/(2e)`

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