If y=log2(log2x),then dydx=

y=log(log2x)log2Diff.dydx=1log2[1log2x×ddx(log2x)]1log2×1logxlog2×ddx[logxlog2].=1logx×1log2×(1x)=1x.logexloge2

If y=log2(log2x),then dydx=

y=log(log2x)log2Diff.dydx=1log2[1log2x×ddx(log2x)]1log2×1logxlog2×ddx[logxlog2].=1logx×1log2×(1x)=1x.logexloge2

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If $y = \log_{2} (\log_{2} x),$ then $\frac{d y}{d x} =$

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$\frac{\log_{2} e}{2 x \log_{e} x}$

$\frac{1}{x \log_{e} x \log_{e} 2}$

$2 \log x$

$\frac{1}{\log_{2} e \log_{e} x}$

answer is B.

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Detailed Solution

$y = \frac{\log (\log_{2} x)}{\log_{2}}$

Diff. $\frac{d y}{d x} = \frac{1}{\log_{2}} [\frac{1}{\log_{2} x} \times \frac{d}{d x} (\log_{2} x)]$

$\frac{1}{\log_{2}} \times \frac{1}{\frac{\log x}{\log_{2}}} \times \frac{d}{d x} [\frac{\log x}{\log_{2}}]$ .

$= \frac{1}{\log x} \times \frac{1}{\log_{2}} \times (\frac{1}{x}) = \frac{1}{x . \log_{e} x {\log_{e}}^{2}}$

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If y=log2(log2x),then dydx=

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If $y = \log_{2} (\log_{2} x),$ then $\frac{d y}{d x} =$