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Q.

If ycos x=xsin y, then dydx=

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a

ysin y+xsin x log yx(cos x-y log x cos y)

b

yx sin xlog x-sin yx(cos x+y log x cos y)

c

ysin y-x log yx( x-y cos y log x)

d

ysin y+x log yx( x+y cos y log x)

answer is A.

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Detailed Solution

detailed_solution_thumbnail

Given ycos x=xsin y Apply log on both sides log(ycos x)=log(xsin y) cos x log y=sin y log x differentiate w.r.to x on both sides cos xydydx+log y(-sin x)=sin yx+log x cosydydx

cos xy-logx cosydydx=sin yx+logy sinx dydx=ysin y+x log y sin xx(cos x-y log x cos y).

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