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Question

xmxmxmx......=ynynyny......, then dydxis equal to:


A

yx

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B

xy

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C

mynx

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D

nymx

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Solution

The correct option is C

mynx


Explanation for the correct option

Given: xmxmx.....∞=ynyny......∞

Let xmxmx.....∞=ynyny......∞=t

Since series is going infinite in power we can write

xmt=yntt=xmxxm....∞andt=ynyny.....∞

Take log on both sides

β‡’logxmt=logynt

β‡’mtlog(x)=ntlog(y)∡logab=bloga

β‡’mlog(x)=nlog(y)

Differentiate with respect to x

β‡’mddx(logx)=nddy(logy)

β‡’m1x=n1ydydx;ddx(logx)=1x

β‡’mynx=dydx

Hence option (c) is the required answer.


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