Q. 174.4( 12 Votes )

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Answer :

Given that


Differentiating with respect to itself, we get





Simplifying, we get


x dx + y dy = x dy – y dx

or


dx(x + y)= dy(x-y)


Hence,


OR


Given that xy-yx=ab


Let u= xy and v= yx, then we get


u-v= ab


Differentiating with respect to x, we get


(Since ab is constant) …. (1)


u= xy


Taking log both sides



Differentiating with respect to x, we get




Hence, ….. (2)


v= yx


Taking log both sides



Differentiating with respect to x, we get






Hence, ……(3)


Substituting (2) and (3) in (1), we get



Simplifying, we get


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