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If (cosx)y=(siny)x, then dydx=

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By Expert Faculty of Sri Chaitanya
a
logsiny+ytanxlogcosxxcoty
b
logsinyytanxlogcosx+coty
c
logsinylogcosx
d
logcosxlogsiny
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detailed solution

Correct option is A

(cosx)y=(siny)x

y.log(cosx)=x.log(siny)

y.1cosx(sinx)+y'.log(cosx)=xcosysiny.y'+log(siny)

y|[logcosxx.cosysiny]=y.sinxcosx+log(siny)

y|[logcosxxcoty]=y.tanx+log(siny)

y|=logsiny+ytanxlogcosxx.coty


ctaimg

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