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Question

Differentiate the following functions with respect to x :

1+log x1log x

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Solution

We have,

ddx(1+log x1log x)

using quotient rule,

(1log x)ddx(1+log x)(1+log x)ddx(10log x)(1log x)2

=(1log x)×1x(1+log x)(1x)(1log x)2=1log x+1+log xx(1log x)2=2x(1log x)2


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